Technical Concepts: April 2010

Saturday, April 24, 2010

Network 2

What are 10Base2, 10Base5 and 10BaseT Ethernet LANs ?
What is the difference between an unspecified passive open and a fully specified passive open
Explain the function of Transmission Control Block
What is a Management Information Base (MIB)
What is anonymous FTP and why would you use it?
What is a pseudo tty?
What is REX?
What does the Mount protocol do ?
What is External Data Representation?
What is the Network Time Protocol?
What is a DNS resource record?
What protocol is used by DNS name servers?
What is the difference between interior and exterior neighbor gateways?
What is the HELLO protocol used for?
What are the advantages and disadvantages of the three types of routing tables?
What is source route?
What is RIP (Routing Information Protocol)?
What is SLIP (Serial Line Interface Protocol)?
What is Proxy ARP?
What is OSPF?
What is Kerberos?
What is a Multi-homed Host?
What is NVT (Network Virtual Terminal)?
What is Gateway-to-Gateway protocol?
What is BGP (Border Gateway Protocol)?
What is autonomous system?
What is EGP (Exterior Gateway Protocol)?
What is IGP (Interior Gateway Protocol)?
What is Mail Gateway?
What is wide-mouth frog?
What are Digrams and Trigrams?
What is silly window syndrome?
What is region?
What is multicast routing?
What is traffic shaping?
What is packet filter?
What is virtual path?
What is virtual channel?
What is logical link control?
Why should you care about the OSI Reference Model?
What is the difference between routable and non- routable protocols?
What is MAU?
Explain 5-4-3 rule.
What is the difference between TFTP and FTP application layer protocols?
What is the range of addresses in the classes of internet addresses?
What is the minimum and maximum length of the header in the TCP segment and IP datagram?
What is difference between ARP and RARP?
What is ICMP?
What are the data units at different layers of the TCP / IP protocol suite?
What is Project 802?
What is Bandwidth?
Difference between bit rate and baud rate?
What is MAC address?
What is attenuation?
What is cladding?
What is RAID?
What is NETBIOS and NETBEUI?
What is redirector?
What is Beaconing?
What is terminal emulation, in which layer it comes?
What is frame relay, in which layer it comes?
What do you meant by “triple X” in Networks?
What is SAP?
What is subnet?
What is Brouter?
How Gateway is different from Routers?
What are the different type of networking / internetworking devices?
What is mesh network?
What is passive topology?
What are the important topologies for networks?
What are major types of networks and explain?
What is Protocol Data Unit?
What is difference between baseband and broadband transmission?
What are the possible ways of data exchange?
What are the types of Transmission media?
What are the types of Transmission media?
What is point-to-point protocol?
What are the two types of transmission technology available?
Difference between the communication and transmission?
What is a different between switch and Hub?
What are the Advantages and Disadvantages of DHCP?
What is Recovery Console?
What is ERD(Emergency Repair Disk)?
What is the difference between POP3 and IMAP Mail Server?
what is .ost file?
Whatz the difference between DNS and WINS?
How can we create VPN to connect to branch office of the same office.what would be the priliminary requirment?
Why should we care about the OSI Reference Model ? What is the main purpose for creating this osi model? why it is a layered model?
What is layer-3 switch?
What is an email client? what is differnce between email client and web mail?
what is the vlan ? how it is work?
Name three network tools used to determine where a network connectivity is lost between two sites A&B.
Which protocol is used for retrieving mails?
What is piggy backing?
What is the default subnet mask for an ipv6 address ?
What is fragmentation of a packet ?
What is MTU of a link ?
Name any field of IP header that can prevent a packet to loop infinitely ?
Under what situations a packet can go into infinite loop in a network ?
Describe a 3-way TCP/IP Handshake.

OS 3

What are the basic functions of an operating system? - Operating system controls and coordinates the use of the hardware among the various applications programs for various uses. Operating system acts as resource allocator and manager. Since there are many possibly conflicting requests for resources the operating system must decide which requests are allocated resources to operating the computer system efficiently and fairly. Also operating system is control program which controls the user programs to prevent errors and improper use of the computer. It is especially concerned with the operation and control of I/O devices.
Why paging is used? - Paging is solution to external fragmentation problem which is to permit the logical address space of a process to be noncontiguous, thus allowing a process to be allocating physical memory wherever the latter is available.
While running DOS on a PC, which command would be used to duplicate the entire diskette? diskcopy

What resources are used when a thread created? How do they differ from those when a process is created? - When a thread is created the threads does not require any new resources to execute the thread shares the resources like memory of the process to which they belong to. The benefit of code sharing is that it allows an application to have several different threads of activity all within the same address space. Whereas if a new process creation is very heavyweight because it always requires new address space to be created and even if they share the memory then the inter process communication is expensive when compared to the communication between the threads.
What is virtual memory? - Virtual memory is hardware technique where the system appears to have more memory that it actually does. This is done by time-sharing, the physical memory and storage parts of the memory one disk when they are not actively being used.
What is Throughput, Turnaround time, waiting time and Response time? - Throughput – number of processes that complete their execution per time unit. Turnaround time – amount of time to execute a particular process. Waiting time – amount of time a process has been waiting in the ready queue. Response time – amount of time it takes from when a request was submitted until the first response is produced, not output (for time-sharing environment).
What is the state of the processor, when a process is waiting for some event to occur? - Waiting state
What is the important aspect of a real-time system or Mission Critical Systems? - A real time operating system has well defined fixed time constraints. Process must be done within the defined constraints or the system will fail. An example is the operating system for a flight control computer or an advanced jet airplane. Often used as a control device in a dedicated application such as controlling scientific experiments, medical imaging systems, industrial control systems, and some display systems. Real-Time systems may be either hard or soft real-time. Hard real-time: Secondary storage limited or absent, data stored in short term memory, or read-only memory (ROM), Conflicts with time-sharing systems, not supported by general-purpose operating systems. Soft real-time: Limited utility in industrial control of robotics, Useful in applications (multimedia, virtual reality) requiring advanced operating-system features.
What is the difference between Hard and Soft real-time systems? - A hard real-time system guarantees that critical tasks complete on time. This goal requires that all delays in the system be bounded from the retrieval of the stored data to the time that it takes the operating system to finish any request made of it. A soft real time system where a critical real-time task gets priority over other tasks and retains that priority until it completes. As in hard real time systems kernel delays need to be bounded
What is the cause of thrashing? How does the system detect thrashing? Once it detects thrashing, what can the system do to eliminate this problem? - Thrashing is caused by under allocation of the minimum number of pages required by a process, forcing it to continuously page fault. The system can detect thrashing by evaluating the level of CPU utilization as compared to the level of multiprogramming. It can be eliminated by reducing the level of multiprogramming.
What is multi tasking, multi programming, multi threading? - Multi programming: Multiprogramming is the technique of running several programs at a time using timesharing. It allows a computer to do several things at the same time. Multiprogramming creates logical parallelism. The concept of multiprogramming is that the operating system keeps several jobs in memory simultaneously. The operating system selects a job from the job pool and starts executing a job, when that job needs to wait for any i/o operations the CPU is switched to another job. So the main idea here is that the CPU is never idle. Multi tasking: Multitasking is the logical extension of multiprogramming .The concept of multitasking is quite similar to multiprogramming but difference is that the switching between jobs occurs so frequently that the users can interact with each program while it is running. This concept is also known as time-sharing systems. A time-shared operating system uses CPU scheduling and multiprogramming to provide each user with a small portion of time-shared system. Multi threading: An application typically is implemented as a separate process with several threads of control. In some situations a single application may be required to perform several similar tasks for example a web server accepts client requests for web pages, images, sound, and so forth. A busy web server may have several of clients concurrently accessing it. If the web server ran as a traditional single-threaded process, it would be able to service only one client at a time. The amount of time that a client might have to wait for its request to be serviced could be enormous. So it is efficient to have one process that contains multiple threads to serve the same purpose. This approach would multithread the web-server process, the server would create a separate thread that would listen for client requests when a request was made rather than creating another process it would create another thread to service the request. To get the advantages like responsiveness, Resource sharing economy and utilization of multiprocessor architectures multithreading concept can be used.
What is hard disk and what is its purpose? - Hard disk is the secondary storage device, which holds the data in bulk, and it holds the data on the magnetic medium of the disk.Hard disks have a hard platter that holds the magnetic medium, the magnetic medium can be easily erased and rewritten, and a typical desktop machine will have a hard disk with a capacity of between 10 and 40 gigabytes. Data is stored onto the disk in the form of files.
What is fragmentation? Different types of fragmentation? - Fragmentation occurs in a dynamic memory allocation system when many of the free blocks are too small to satisfy any request. External Fragmentation: External Fragmentation happens when a dynamic memory allocation algorithm allocates some memory and a small piece is left over that cannot be effectively used. If too much external fragmentation occurs, the amount of usable memory is drastically reduced. Total memory space exists to satisfy a request, but it is not contiguous. Internal Fragmentation: Internal fragmentation is the space wasted inside of allocated memory blocks because of restriction on the allowed sizes of allocated blocks. Allocated memory may be slightly larger than requested memory; this size difference is memory internal to a partition, but not being used
What is DRAM? In which form does it store data? - DRAM is not the best, but it’s cheap, does the job, and is available almost everywhere you look. DRAM data resides in a cell made of a capacitor and a transistor. The capacitor tends to lose data unless it’s recharged every couple of milliseconds, and this recharging tends to slow down the performance of DRAM compared to speedier RAM types.
What is Dispatcher? - Dispatcher module gives control of the CPU to the process selected by the short-term scheduler; this involves: Switching context, Switching to user mode, Jumping to the proper location in the user program to restart that program, dispatch latency – time it takes for the dispatcher to stop one process and start another running.
What is CPU Scheduler? - Selects from among the processes in memory that are ready to execute, and allocates the CPU to one of them. CPU scheduling decisions may take place when a process: 1.Switches from running to waiting state. 2.Switches from running to ready state. 3.Switches from waiting to ready. 4.Terminates. Scheduling under 1 and 4 is non-preemptive. All other scheduling is preemptive.
What is Context Switch? - Switching the CPU to another process requires saving the state of the old process and loading the saved state for the new process. This task is known as a context switch. Context-switch time is pure overhead, because the system does no useful work while switching. Its speed varies from machine to machine, depending on the memory speed, the number of registers which must be copied, the existed of special instructions(such as a single instruction to load or store all registers).
What is cache memory? - Cache memory is random access memory (RAM) that a computer microprocessor can access more quickly than it can access regular RAM. As the microprocessor processes data, it looks first in the cache memory and if it finds the data there (from a previous reading of data), it does not have to do the more time-consuming reading of data from larger memory.
What is a Safe State and what is its use in deadlock avoidance? - When a process requests an available resource, system must decide if immediate allocation leaves the system in a safe state. System is in safe state if there exists a safe sequence of all processes. Deadlock Avoidance: ensure that a system will never enter an unsafe state.
What is a Real-Time System? - A real time process is a process that must respond to the events within a certain time period. A real time operating system is an operating system that can run real time processes successfully

EEE 3 bluetooth

Why is Bluetooth called a cable replacement technology?
Give a generic description of Bluetooth?
Why can Bluetooth equipment integrate easily in TCP/IP network?
Is it possible to connect multiple Bluetooth hubs?
What is FCC and how does it relate to Bluetooth?
Under what frequency range does Bluetooth work?
Do Bluetooth devices need line of sight to connect to one another?
Which technology is used in Bluetooth for avoiding interference?
What is Airport?
What is Piconet?
What is FEC in Bluetooth?
Which method is primarily used for Voice transfer?
What is the frequency range used for Bluetooth in Europe and United States?
List some Technology characteristic of Bluetooth?
Which company originally conceived and developed Bluetooth?
How does Bluetooth use frequency hopping for security?
What is a Bluetooth dongle?
What are the other (competing or not) wireless technologies?
Which Bluetooth version uses adaptive frequency hopping? Why?
How many SCO links are there in a piconet?
what is the total number of masters and slaves in a piconet?
Which method is used for Data transfer?
What is the frequency range used for Bluetooth in Japan?
What is the strength of the signal transmitted by powerful cell phones?
What is RJ-45 and full name of RJ-45?
What is LDAP? Where all can it be used
Difference between TCP and UDP
What is 802.11b, Bluetooth
What types of routing are possible in a wireless network
How does traceroute work
What are the different types of routing possible at layer 3
Explain TCP connection establishment and tear down
What is ICMP, ARP, Multicast, Broadcast
When are packets passed from TCP layer to application layer? What if some IP packets are lost
Describe TCP flow control
Explain DNS, IP address allocation
What is IP Spoofing? What do hackers do with it
What is DOS attack
Explain SSL
How can you keep a TCP connection from tearing down when no data will be sent for a long time?

EEE 2 Microprocessors

What are the flags in 8086? - In 8086 Carry flag, Parity flag, Auxiliary carry flag, Zero flag, Overflow flag, Trace flag, Interrupt flag, Direction flag, and Sign flag.
What are the various interrupts in 8086? - Maskable interrupts, Non-Maskable interrupts.
What is meant by Maskable interrupts? - An interrupt that can be turned off by the programmer is known as Maskable interrupt.

What is Non-Maskable interrupts? - An interrupt which can be never be turned off (ie.disabled) is known as Non-Maskable interrupt.
Which interrupts are generally used for critical events? - Non-Maskable interrupts are used in critical events. Such as Power failure, Emergency, Shut off etc.,
Give examples for Maskable interrupts? - RST 7.5, RST6.5, RST5.5 are Maskable interrupts
Give example for Non-Maskable interrupts? - Trap is known as Non-Maskable interrupts, which is used in emergency condition.
What is the Maximum clock frequency in 8086? - 5 Mhz is the Maximum clock frequency in 8086.
What are the various segment registers in 8086? - Code, Data, Stack, Extra Segment registers in 8086.
Which Stack is used in 8086? - FIFO (First In First Out) stack is used in 8086.In this type of Stack the first stored information is retrieved first.
What are the address lines for the software interrupts? -

RST 0	0000 H
RST1	0008 H
RST2	0010 H
RST3	0018 H
RST4	0020 H
RST5	0028 H
RST6	0030 H
RST7	0038 H

What is SIM and RIM instructions? - SIM is Set Interrupt Mask. Used to mask the hardware interrupts. RIM is Read Interrupt Mask. Used to check whether the interrupt is Masked or not.
Which is the tool used to connect the user and the computer? - Interpreter is the tool used to connect the user and the tool.
What is the position of the Stack Pointer after the PUSH instruction? - The address line is 02 less than the earlier value.
What is the position of the Stack Pointer after the POP instruction? - The address line is 02 greater than the earlier value.
Logic calculations are done in which type of registers? - Accumulator is the register in which Arithmetic and Logic calculations are done.
What are the different functional units in 8086? - Bus Interface Unit and Execution unit, are the two different functional units in 8086.
Give examples for Micro controller? - Z80, Intel MSC51 &96, Motorola are the best examples of Microcontroller.
What is meant by cross-compiler? - A program runs on one machine and executes on another is called as cross-compiler.
What are the address lines for the hardware interrupts? -

RST 7.5	003C H
RST 6.5	0034 H
RST 5.5	002C H
TRAP	0024 H

Which Segment is used to store interrupt and subroutine return address registers? - Stack Segment in segment register is used to store interrupt and subroutine return address registers.
Which Flags can be set or reset by the programmer and also used to control the operation of the processor? - Trace Flag, Interrupt Flag, Direction Flag.
What does EU do? - Execution Unit receives program instruction codes and data from BIU, executes these instructions and store the result in general registers.
Which microprocessor accepts the program written for 8086 without any changes? - 8088 is that processor.
What is the difference between 8086 and 8088? - The BIU in 8088 is 8-bit data bus & 16- bit in 8086.Instruction queue is 4 byte long in 8088and 6 byte in 8086.

Friday, April 23, 2010

1.    What is meant by D-FF?
2.    What is the basic difference between Latches and Flip flops?
3.    What is a multiplexer?
4.    How can you convert an SR Flip-flop to a JK Flip-flop?
5.    How can you convert an JK Flip-flop to a D Flip-flop?
6.    What is Race-around problem? How can you rectify it?
7.    Which semiconductor device is used as a voltage regulator and why?
8.    What do you mean by an ideal voltage source?
9.    What do you mean by zener breakdown and avalanche breakdown?
10.    What are the different types of filters?
11.    What is the need of filtering ideal response of filters and actual response of filters?
12.    What is sampling theorem?
13.    What is impulse response?
14.    Explain the advantages and disadvantages of FIR filters compared to IIR counterparts.
15.    What is CMRR? Explain briefly.
16.    What do you mean by half-duplex and full-duplex communication? Explain briefly.
17.    Which range of signals are used for terrestrial transmission?
18.    What is the need for modulation?
19.    Which type of modulation is used in TV transmission?
20.    Why we use vestigial side band (VSB-C3F) transmission for picture?
21.    When transmitting digital signals is it necessary to transmit some harmonics in addition to fundamental frequency?
22.    For asynchronous transmission, is it necessary to supply some synchronizing pulses additionally or to supply or to supply start and stop bit?
23.    BPFSK is more efficient than BFSK in presence of noise. Why?
24.    What is meant by pre-emphasis and de-emphasis?
25.    What do you mean by 3 dB cutoff frequency? Why is it 3 dB, not 1 dB?
26.    What do you mean by ASCII, EBCDIC?

Aptitude 5

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1. The distance between the points (3, -4) and (3, 3) is
     7 Units   5 Units   6 Units   8 Units

2. The coordinates of a point which divide the join of A (5, 5) and (8, 5) in the ratio 2 : 1 are
     (5, 6)   (7, 5)   (8,4)    (9, 6)

3. XYZ is an equilateral triangle with vertices X (6, -2), Y (2, - 1) and Z (4, -2). If ZA is one of its medians find the length of the median.
     sqrt6 Units sqrt5 Units sqrt13 Units sqrt10 Units

4. The ratio in which the line segment joining P (3. –4) and Q(6, 7) is divided by x axis is
     5 : 2   3 : 4 2 : 3   4 : 7

5. P ( - 4, b ) and Q ( 2, b + 2 ) are 2 points and the co-ordinates of the middle point of PQ are ( - 2, 2) . The value of b is
     1   3   -2   -1

6. The slope of the line Joining A (-4. 6) and B (5, 3) is
     2/5 -1/3   2/3   1/3

7. The points of intersection of the circle x2 +y2 = 34 and line y = 5
    (2, 4 ) ( -2, 4)   (3, 6) (-3, 6)   (3, 5) (3, -5)   (2, 3) (-2, 3)

8. Complete the series 25, 125, 36, 216, 49, ____
     200   290   335 343

9.The value of a machine depreciates at the rate @ 15% per annum. If the price of a new machine is Rs. 60,000 its value after 2 years will be
     Rs. 43350    Rs.45000   Rs. 52570   Rs. 51750

10. 80% of p = 40% of Q and Q = X % P . Then the value of x is
     360   200   300   250

11.The population of a town increase by 10% every year. If it is 16093 row, its population 2 year ago was
    13300    14200   14750   15265

12. If A:B is 2:3 and B:C is 3:4 then A:C is equal to
     2:3 6:7 5:6   1:2

13. If the numerator of a fraction is increased by 15 % and the denominator is increased by 10% , then the value of the fraction is 15/26, The original fraction is
    130/223   158/229   133/462   165/299

14. X varies directly as Y varies and Z varies inversely as Y varies . At a time Y = 10, X = 20 , Z
= 5 , If y is changed to 20 then the values of Z is :
     2.5   5   10   3

15. If a Box containing 10 mirrors is dropped which of the following can not be the ratio of broken mirrors to unbroken mirrors.
     1 : 1   2 : 3   3 : 2   3 : 4

16. 5 (P ‘s Capital ) = 10 (Q’s Capital ) = 15 ( R’s Capital ) then the ratio of their capital is :
     6 : 3 : 2   2 : 7 : 9   8 : 5 : 3 2 : 3 : 1

17. The difference between a discount of 50 % on Rs. 500 and two successive discounts of 45 % and 5% on the same amount is
     Rs 15 Rs 11.25   Rs 10   None of These

18. A man rows upstream 10 Km. And downstream 20 Km taking 4 hrs each time. The velocity of the current is
     2 Kmph   2.5 Kmph 1.25 Kmph 1. 5 Kmph

19.A boat goes 50 Km upstream in 10 hours and a distance of 40 Km. Down stream is 9 hours. The speed of the boat in standing water is
    4.9 Kmph 5.2 Kmph 4.5 Kmph4.72 Kmph

20. A man can swim 4 Kmph in still water . If the velocity of the stream be 3 kmph the time taken by him to swim to a place 14 Km upstream and back is:
    16 Hours 12 Hours 14 Hours 10 Hours

21. D xyz is rotated about x y as axis. Find the volume of the solid generated if
xy = 6 cm and yz = 10 cm. D x y z is a right angled D
    200 P   300 P     250 P   60 P

22. I shopped in 4 shops 1 after another. In the end I had no money. In each shop I
Spent Rs 2 more than 20% of what I had when I entered each shop. How much
did I have in the beginning .
     87.81   82.35   80.30   85.65

23. A rides 5 km at 1 kmph, 4 km at 2 kmph and 12 km at 6 kmph. What is his Average speed .
    2.33 kmphr. 4.33 kmphr. 3.33 kmphr. 1.33 kmp hr.

24. Within a square ground with one side 20 m , there is a square path that is 4 m in breadth. What is the area of the park without the path.
    144 m2   400 m2   16 m2   Not determined.

25. If ( p - q) 2 = ( x – y ) 2, then x =
     p – q + y   y – p + q   Both ( a) and (b)   None of these

26. Rs. 13400 are invested at SI for 7 years partly at 6 % interest and partly at 4 % interest. If both sums yield equal linterest , find the sum invested at 6 %.
     Rs. 5360 Rs. 3000 Rs. 4000 Rs. 2800

27. B reaches 10 ,minutes early travelling at 6 km per hour, whereas A reaches 10 minutes late travelling at 5 km per hour. Find the distance.
    10 Km   12 Km   17 Km   20 Km

28. Fi nd the next term in the series 123, 129, 141, 147, ____________
     171 162   159 148

29. A 2 digit number is divisible by 6 and not by 12. When the digits are interchanged the number
is also divisible by 12. The absolute value of the difference between the numbers is
     18   12   24   36

30. A Farmer notices that the area of his farm in sq mts is equal to 2 times the square of the number of tractors he owns. If one tractor is stolen he has to sell 62 sq mts of the farm. So as to maintain the relationship. Find the number of tractors remaining.
     14 15   16   17

31. How many numbers greater than a million can be formed using digits 0,6 ,6, 7 , 0, 0 , 6,
and 7 ?
     410 420   360 800

32. At exactly midnight, a thief tries to steal a car from a garage. 2 full minutes are gone before the guard arrives at the scene and starts running after the burglar. At 12 : 05 :00, the burglar panicks and slips. By the time he gets up, 10 seconds are gone and the guard has caught up with him . Had he not fallen, the thief would have reached a safe hideout which was at a distance of 3560 m from the museum at 12 : 05 : 56 hours. What was the running speed of the security guard ?
     15.07 m / sec 0.6 km / min 12 m / sec 15 m / sec

33. X and Y enter into a partnership by investing certain capital in the ratio of 1 : 3. However, after 4 months, X alone starts managing the business and Y pays him Rs. 10,000 per month. How much profit should they make so that at the end of the year, when the profit is divided, the net incomes of both are the same for the year ?
     Rs. 40,000   Rs.320,000   Rs 400, 000 Rs . 200, 000

34. Complete the series 1, 3, 4, 13, 53, ____

     690   670    65    35

35. There are 5 people - A, B, C, D, E, standing in a queue. How many ways are available to form the queue such that D is not ahead of E ?
     60   120   125   80

36. 5 men can dok a certain task working 10 hours a day in 1 day that requires 4 Women 2 days working 8 hours a day and 5 boys 4 days working 5 hours a day. If a contractor hires 20 men, 9 Women, and 10 boys to complete together 1000 such tasks, starting on 1st March, 2000, when will the entire work get over ?
     2 nd July    29 th June   30 th June   4 th August

37. X's Salary is 150% of Y's salary. Z's salary is 75 % of Y's salary. The total of all three salaries is Rs. 325,000. How Much is Y's Salary ?
     Rs. 100,000 Rs. 25, 0000 Rs. 24, 000 Rs. 28, 000

38. If santa can walk a certain distance in 200 days when he rests 18 hours each day; how long will it take to walk twice the distance twice as fast and the rest half as long each day ?
     80 days   40 days   100 days   50 days

39. An automobile has two punctured tyres. The first puncture by itself would make the tyre flat in 10 minutes. The second puncture by itself would make the tyre flat in 5 minutes. How long would it take for both punctures together to make the remaining tyre flat ?
     2 1/3 minutes   4 minutes   5 minutes   15 minutes

40. a * b = a - b, if both 'a ' and ' b ' are positive.
= 1 otherwise
a @ b = ab, if ' ab ' is positive.
= 0 otherwise
based on the data given above solve the question given below

[ 4 * ( - 5 ) ] @ [ ( - 2 ) * 2 ] /[ (- 4 ) @ (- 5 )] * [ 2 @ 2 ]

     1/16   1/4 1/8     0

41. The square root of (11 + 2 sqrt(30) ) is
     sqrt5 + sqrt6     sqrt 5 +sqrt3     sqrt 10 + sqrt3    sqrt 6 + 1

42. An army chief wishing to draw his 17164 men in the form of a solid square found that he had 3 men more. The number of men is the last row was.
     152   131   134   140

43. What is the ratio whose terms differ by 50 and the measure of which is 3 / 5
     80    95    60     75

44. A bag contains Rs 300 in the form of 1 rupee, 50 paise and 25 paise coins in the ration 3 : 2 : 4 The number of 25 paise coins in the bag are
     240   300   360 180

45. Rs. 11250 are divided among Jay , Ajay & Vijay so that Jay may receive one fourth as much as Ajay and Vijay together receive and Ajay one half of what Jay & Vijay together receive . What is Jay’s share.
    Rs 6500 Rs 5250   Rs 2250   Rs 3750

46. X, Y, Z, enter into a partnership. X invests some money at the beginning y, invests 4 times
The amount after 8 months and Z invests 3 times the amount after 10 months. If the annual profit be Rs. 8500 then Z’s share is
     1525   1875   2000 1500

47. By selling 75 toys a shopkeeper gains the selling price of 25 toys. Find his gain percent.
     20%   25%   50% 75%

48. P & Q enter into a partnership P invests Rs 8000 for 6 months and Q remains in the
Business for 3 months. Out of the total profit Q claims ½ of the profit. What was Q’s contribution
     Rs 5750 Rs 15525 Rs 8000 Rs 16000

49. Successive discounts of 25% and 15% are equivalent to a single discount of
     42.75% 40% 36.25% 35%

50.If 4 cars are sold at the cost price of 6 cars the profit % will be
     50% 33 1/3% 16.67% 32%

QUANTITATIVE APTITUDE TEST PAPER 4 : EXPLANATORY ANSWERS

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1. Required distance = sqrt (3-3) 2 + (3 – (- 4) 2 )
= sqrt (7) 2
= 7 Units.
Hence[1]

2. The required point is
[ 2 * 8 + 1 * 5 / 2 + 1 , 2 * 5 + 1 * (- 3 ) / (2 + 1) ]
= 21 / 3, 15 / 3
= ( 7 , 5)
Hence[2]

3. A is the midpoint of yz,
The coordinates of A are [ 2+4 / 2 , - 2 + 4 / 2 , -2 + 2 / 2 ]
= ( 3 , 0)
XA = sqrt (6 – 3) 2 + ( - 2 – 0 ) 2
=sqrt 3 2 + 2 2
= sqrt 9 + 4 = sqrt 13 Units
Hence[3]

4. Let the ratio be K : 1
TK + 1 * ( - 4 ) / K + 1 = 0
TK = 4
K = 4 / 7
The ratio is 4/7 : 1
= 4 : 7
Hence [4]

5. b + b + 2 / 2 = 2
2b + 2 = 4
2b = 2
b = 1
Hence[1]

6. Slope = y 2 - y1 / x2 - x1
= 3 - 6 / 5 + 4 = -3 / 9 = -1/3
Hence[2]

7. Putting y = 5 in x 2 + y 2 = 34
= x 2 + 25 = 34
x 2 = a \ x = ± 3
points are ( 3 , 5 ) and ( 3, -5)
Hence[3]

8. The series is 52, 53, 62 and so on

9. Value of Machinery after 2 years = 60000 ( 1 – 15 / 100) 2
60000 ( 115 / 100) 2
= Rs 43350
Hence[1]

10. 8 0 / 100 P = 40 / 100 Q = 40 / 100 * X/100
8 / 10 = 4 x / 1000
X = 8000 / 40 = 200
Hence[2]

11. Population 2 years ago = 16093 / (1 + 10 / 100 ) 2
= 16093 * 10000 / 12100
= 13300
Hence[1]

12. A:C = 2/3 * 3/4
=1:2
Hence[4]

13. Let the fraction be x/y
New fraction = 115% of x / 110% of y = 23x / 22y = 15 / 26
x / y = ( 15/26 * 22 / 23 ) = 330 / 598 = 165 / 299
Hence[4]

14. When y = 10, X = 20, Z = 5
x = k, and z = k 2 / y 5 = k 2 / 10
K 2 = 50
X = 2y and Z = 50 / y
When y = 20
Z = 50 / 20 = 2.5
Hence[1]

15. For a perfect division into whole numbers the sum of the terms of the ratio must divide 10 Therefore the ratio cannot be 3 : 4
Hence[4]

16. SP = 10 , Q = 15 , R = x
P = x / 5, Q = x / 10 and R = x / 15
P : Q : R = x /5 : x / 10 : x / 15
= 6 : 3 : 2
Hence[1]

17. S.P at 50% discount = Rs 250
S.P. after 2 successive discounts of 5 % and 5% = 95% of ( 55% of 500) =
[ 95 / 100 * 55 / 100 * 500 ]
= Rs. 261.25
differences = Rs 11.25
Hence[2]

18. Rate unstream = 10 / 4 = 2.5 kmph
Rate downstream = 20 / 4 = 5 kmph
velocity of current = 1 / 2 ( 5 - 2.5 ) kmph
= 1.25 kmph
Hence[2]

19. Rate upstream = 50 / 10 = 5 kmph
Rate downstream = 40 / 9 = 4.44 kmph
Rate in still water = 1 / 2 ( 5 * 4.44)
= 4.72 kmph
Hence[4]

20. Rate upstream = 1
rate downstream = 7
Total time take = [ 14 / 1 + 14 / 7]
= 14 + 2 = 16 hours
Hence[1]

21. A cone is generated with radius 10 cm & vertical height = 6 cm
Volume = 1 P / 3 * 100 * 6 = 200 P
Hence [ 1 ]

22. Let him have Rs. X when he intered the Amount spent = 2 + x / 5
x – 2 – x / 5 = 0
5x - 10 – x = 0
4x = 10 , x = 2.5
When I entered the 3rd shop, I had 2.5 ( 2.5 + 2 ) = 11.25
When I entered the 2nd shop I had 11.25 + 2 ( 2.5) = 33.125
When I entered the 1st shop I had 33.125 + 2 (2.5) = 87.8125
Hence [1]

23. Total time = 5 / 1 + 4 / 2 + 12 / 6
= 9 hours
Total distance = 21 km
Average speed = 21 / 9 = 2.33 every hr.
Hence[1]

24. It cannot be determined as it depends on the position of the path. Hence[4]

25. ( p - q ) 2 = ( x – y ) 2
p - q = ± x – y
p – q = x - y or y – x
x = p - q + y or q - p + y
Hence [3]

26. Let the sum interested at 6% be x
X * 7 * 6 / 100 = 100
= ( 13400 – x ) * 7 * 4 / 100
42 x / 10 = 93800 – 7x / 25
42 x = 93800 * 4 - 28 x
70 x = 93800 * 4 / 70 = Rs 5360
Hence[1]

27. Let ‘d ‘ be the distance and t’ be the normal time
D / 6 = t – 10 / 60
D / 5 = t + 10 / 60
D / 6 - d / 5 = - 10 / 60 - 10 / 60
5d – 6d / 30 = -20 / 60
-2d = -20
d = 10 km
Hence [ 1 ]

28. Each number in the series in the precious numbers added to the sum of its digits.
the last no. = 1 + 4 + 7 + 147
= 159
Hence [ 3 ]

29. Both the digits must be even and odd multiples of 6 will not be divisibleby 12
The number is 42
And its reverse is 24
The difference = 18
Hence [ 1 ]

30. Let there be x tractors
Area of farm = 2x 2
When one tractor is stolen x – 1 will
Remain 2x 2 - 2(x – 1) 2 = 62
Solving
2x 2 - 2 (x 2 - 2x + 1) = 62
2x 2 - 2x 2 + 4x - 2 = 62
4x = 60
x = 15
No. of tractors = 15 - 1 = 14
Hence [ 1 ]

31. All seven digits with have to be used to make a number greater than a million.
Since there are 3 6’s and 2 7’s the number of distinct persutations = 7! / 2! 3!
But all persutations starting with zero should let be counted
7! / 2! 3! - 5! / 2! 3!
= 410
Hence [1]

32. Let the speed of the burglar and the guard be ‘x’ min /sec and ‘y’ min / sec
The guard covered the distance in 3min 10 sec for which the thief took 5 minutes
Therefore 300 x = 190 Y
30x = 19y
Also given that
356 * x = 3560 m
x = 10 m / sec
and y = 300 * 10 / 190 = 15.07 m / sec
Hence [ 1 ]

33. Let profit be Rs p
Then x gets 0.25 p. and y gets 0.75 p. in the ratio of their investement.
Y pay Rs. 10, 000 per month for 8 months
= 10000 * 8 = Rs 80, 000
= 0.25 p + 80000 = 0.75 p - 80000
0. 5 p = 160000
P = 320, 000
Hence [2]

34. The series is 3*1+1, 4*3+1 and so on

35. For any positions of A B & C there are 2 ways of completing the queue either D willl be
ahead or behind E since of the total combinations of forming a queue half will have D ahead
of E.
Total No. of ways = 5! = 120
But in this case = 60
Hence[ 1 ]

36. One task = 5 men 10 hrs 1 day = 50 - man hours
same task = 4 women 8 hrs 2 days = 64 - women hours
same tassk = 5 boys 5 hrs 4 days = 100 - boy hours
each day total labour available = 20 men = (200 man hours) + 9 women (72 women hours ) + 10 boys = 50 boy hours
200 * 100 / 50 + 72 * 100 / 64 + 50
= 400 + 150 + 50
= 600 boy hours

boy hours   task   days

100            1           1
600         1000        ?
= 1000 * 100 / 600 = 167 days
from 1st march 167 days = 14 th August.
Hence [ 4 ]

37. Let y’s salary be x
x’s salary = 150 x
z’s salary = 75 x / 100
x + 75 x / 100 + 150x / 100 = 325 x / 100
325x / 100 = 3, 25, 000
x = 325000 * 100 / 325 = 1, 00, 000.
[ Hence ]

38. Distance Time Speed Days
x 24 - 18 = 6 hrs y 200
2x 24 - 9 = 15 hrs 2y ?
Days = 200 * 2x / x * 6 / 15 * y / 2y = 80 days.
Hence [ 1 ]

39. In 1 minute, tyre flat = 1 / 10 -------- Puncture (I)
In 1 minute, tyre flat = 1 / 5 -------- puncture (II)
Together 1 / 10 + 1 / 5 = 3 / 10 in one minute
Remaining = 7 / 10
= 7 / 10 * 10 / 3 = 7 / 3
= 2 1/ 3 minutes
Hence[1]

40. ( 1 ) ( 1 ) / 20 – 4 = 1 / 16
Hence [1]

41. Two numbers whose sum is 11 and product of their squares is 30 are sqrt 5 & sqrt 6
sqrt 11 + 2 sqrt 30
= sqrt ( sqrt 5 + sqrt 6 ) 2
= ( sqrt5 + sqrt 6 )
Hence [ 1 ]

42. 17164 - 3 = 17161
sqrt 17161 = 131
No. of men in the last row was 131
Hence [ 2 ]

43. Let the term be x : x + 50
X / x + 50 = 3 / 5
5x = 3x + 150 = 2x = 150
x = 75
Hence [4]

44. The ratio of coins = 3/1 : 2/2 : 4/4
= 3 : 1 : 1
The amount of 25 paise coins is Rs. 60
No of coins = 60 / 0.25
= 240 coins
Hence [1]

45. J + A + V = 11250
J = ¼ ( A + V )
4 J = A + V
5 J = 11250
J = 11250 / 5 = 2250
Hence [ 3 ]

46. Let x invest Rs a for 12 months Y invest Rs 4a for 4 months Z invest Rs 3a for 2 months
The ratio is 12a : 16a : 6a
Z’s share = Rs 8500 * 3 / 17 = Rs 1500
Hence [ 4 ]

47. S. P of 75 toys = C P of 75 toys
Let CP of each toy = Rs 1
CP of 50 toys = Rs 50
SP of 50 toys = Rs 75
= 25 * 100 / 50
= 50%
Hence [ 3 ]

48.Let Q’s contribution = Rs x
8000 * 6 : 3x
16000 : x
ratio of profit ½ : ½
= 1 : 1
16000 / x = 1 / 1
= Rs 16000
Hence [ 4 ]

49. Let the marked price be Rs. 100
Final SP after 2 discounts = 15%, 75% of Rs 100
= Rs. 63.75
Single discount = 100 - 63.75 = 36.25 %
Hence [ 3 ]

50. Let C.P. of 1 car=x
C.P. of 4 cars=4x
% profit=2x/4x*100
=50%
Hence[1]

Aptitude 4

1. "A game of 50" means a game in which the player scoring 50 points first is the winner. In a game of 50, A can give B 10 points. This means that when A scores 50, B scores 40 points. In a game of 50, A can give B 10 points, but B can give C 20 points. With the same efficiency how many points can A give C?

1] 30
2] 25
3] 40
4] 50

2. 2 pipes X and Y fill a tub in 10 min and 15 min resp. Both are opened and at the end of 5 minutes X is turned off. How much time will the tub take to fill?

1] 3/2 min
2] 1/2 min
3] 4/3 min
4] 5/2 min

3. Walking at 2/3 of his usual speed a man is 2 hrs.late. Find his actual travel time

1] 8 hrs
2] 4hrs
3] 3hrs
4] none of these

4. A train after travelling 30 km from X meets with an accident and proceeds at 3/4 of the former speed and reaches by 45 min. late. Had the accident happened 10 kms further one, it would have arrived 15 min sooner. Find the original speed and distance.

1] 60km
2] 30 km
3] 50 km
4] 20 km

5. A cat sees a rat 50 metres away from her and moves in the opposite direction at a speed of 12 km/hr. A minute later the rat sees her and gives chase at a speed of 15 km/hr. How soon will the rat overtake her?

1] 5 min
2] 6 min
3] 2 min
4] 12 min

6. 3 pipes can fill a reservoirin 10,15 and 20 hrs. resp. The first was opened at 5 a.m. , the second at 6 a.m., third at 7 a.m. When will the reservoir the filled?

1] 5:20a.m.
2] 6:30 a.m.
3] 10:20 a.m.
4] 4 p.m.

7. Rowing at a steady rate, a man travels downstream for an hour and covers 5 km. If he takes 1hr.20min. For the return journey. Find the speed of the current?

1] 0.625 km/hr
2] 0.325 km/hr
3] 0.75 km/hr
4] none of these

8. If 15 men and 10 boys can do in 1 day as much work as 12 men and 20 boys. How much should a man be paid a day if a boy is to get Rs.10 a day?

1] Rs.30
2] Rs.33.33
3] Rs.40
4] Rs.45

9. A cop after a robber who has 100m start. The cop runs 2 km in 8mins. And the thief 2 km in 12 mins. How far the thief has gone before he overtaken?

1] 200
2] 210
3] 250
4] 300

10. 1The sides of a triangle are 5:6:7 and its area is 800 sqft. Find its sides?

1] Sqrt[800/sqrt(225)]
2] sqrt[800/sqrt(216)]
3] sqrt[800/sqrt(210)]
4 ]sqrt[760/sqrt(220)]

11. Find the area of the cyclic quadrilateral whose sides are 15,12,10 and 13 cms.

1] 30*sqrt(26)
2] 30*sqrt(20)
3] 10*sqrt(6)
4] 10*sqrt(2)

12. Cost of painting the 4 walls of a room 40ft.*15ft. At Rs.5 per square feet is Rs.7500. Find the height of the room?

1] 14 ft.
2]13.63 ft.
3]15.72 ft.
4]21.2 ft.

13. The areas of a trapezium of height 20 cm. Is 800 cm2. One parallel side is
10 cm. Longer than the other. Find the parallel side?

1] 35,45
2] 30,40
3] 45,35
4] 60,70

14. Volume of a right circular cylinder is 450 cm3and its curved surfaces area is 200 cm2. Find its radius?

1] 2.5 cm
2] 1.5 cm
3] 5cm
4] 4.5 cm

15. Iron weighs 8 times the weight of steel . Find the diameter of an iron ball whose weight is equal to that of a ball of steel 16 inches diameter?

1] 6
2] 7.5
3] 9
4] 8

16. A rectangle 5cm*3cm is rotated about its smaller edge as axis. Find the curved surface area and volume of solid generated?

1] 85,60
2] 35,40
3] 75,30
4] 30,75

17. A well 20m in diameter is dug 15m deep and earth is spread all around a width of 5m to form an embankment. Find the height of the embankment.

1] 69
2] 82
3] 80
4] 75

18. The radius of a circular cylinder is increased 40%. Find the % increase in volume?

1] 95
2] 96
3] 72
4] 48

19. A river 10m deep 200m wide flows at the rate of 6km/hr. Find the metric tones of water running into the sea per minute?

1] 30000
2] 10000
3] 2*105
4] 2*104

20. If the diameter of a cylinder is 14cm. And height is 10cm, then total surface area (in cm2) is:

1] 748
2] 896
3] 558
4] 468

21. The radius of a cylinder is 2m. And its length is 20m. The area of an iron sheet constructed from the cylinder is:

1] 88*22/7
2] 80*22/7
3] 36*22/7
4] 54*22/7

22. The sum of the radius of the base and height of a solid cylinder is 40m. If the total surface area of the cylinder is 1760 m2 its volume is:

57003
5420m3
50823
56003

23. the radii of 2 cylinders are in the ratio 3:4. Their heights are in the ration 2:3. The ratio of their volumes is

1] 1:2
2] 2:1
3] 3:4
4] 2:3

24. Two cylinders of equal volume have their heights in the ratio 2:3. Ratio of their radii is

1] 1:4
2] 1:sqrt(2)
3] sqrt(2):1
4] 2:1

25. If a train runs at 20 km/hr, it reaches its destination late by 10 min. But if it runs at 30 km/hr, it is late by 2 min. only. The correct time for the train to complete its journey is:

1] 12 min
2] 8 min
3] 14 min
4] 15 min

26. Two busess travel to a place 20 kmph and 40 kmhr. If the second bus takes 6 hrs. less than the fixed for the journey the length of the journey is:

1] 262 km
2] 240km
3] 200km
4] 271.5km

27. A car travels a distance of 360km at a uniform speed. If speed of the car is 20km/hr more then time is 3 hrs. less.The original speed of car was:

1] 40
2] 45
3] 32
4] 37

28. A man covers 30km partly at 4km/hr and 6km/hr. If he covers former distance 6km/hr and later at 4 km/hr,he could cover 2km more in the some time. Time taken to cover the whole distance in the original time is:

1] 3.75
2] 6.2
3] 5.5
4] 4.7

29. A theif steals a car at 1p.m. and drives it at 20km/hr. The theft is discovered at 2p.m. The owners sets of another car at 30 km/hr, he will overtake the thief at:

1] 3:06p.m
2] 2:52p.m.
3] 4:00p.m.
4] 2:20p.m.

30. 1The ratio between the rate of walking of x and y is 2:3. If the time taken by B to cover a certain distance is 24min, to cover the same distance A will take:

1] 32
2] 48
3] 16
4] 36

31. 125, 106, 89, 76, 65, _____

1] 56
2] 53
3] 58
4] 59

32. 5, 6, 3, 4, 1, ____

1] 2
2] 4
3] -2
4] 6

33. 12, 30, 105, 473, 2599, ____

1] 15913
2] 16892
3] 3654
4] 3564

34. 13,20,140,147,1029, ____

1] 1056
2] 7203
3] 1033
4] 1036

35. The area of a triangle with base 36 cms is equal to the area of a circle of radius 21 cms. Determine the approximate height of the triangle.

1] 77cm
2] 75cm
3] 52 cm
4] 46 cm

36. Pens at 20 Rs each and books at 40 Rs each were purchased. In all these were 6, at a total cost of Rs.180. If the number of Pens and books were interchanged, how much less would have been spent ?

1] 0
2] same amount
3] Rs.2.50
4] Rs.6

37. 123, 211,299,156,244,____

1] 325
2] 250
3] 332
4] none of these

38. 855,7695,69255,623295,_____

1] 5629653
2] 5609655
3] 6609655
4] 1608652

39. An empty jar weighs w1 gm. The jar half filled with a liquid weights w2
gm. Find the weight of the jar. Completely filled with the same liquid.

1] 2(w2-w1)
2] 2w+w1
3] 2w2-w1
4] 2(w2+w1)

40. A person travels the first 1/3 of distance to be covered at a speed of x km/hr, the 2nd 1/3rd at 2x km/hr and the final 1/3rd at 3x km/hr. What is the average speed for the entire journey?

x km/hr
1/2*x km/hr
2/3*x km/hr
18/11*x km/hr

41. Triangle PQR is an isosceles triangle in which the sides in which the sides xy and xz are 15 each and the base yz is 18. ABCD is a squar, the side AB being on yz and cd in xz and xy resp. Find the area of ABCD?

1] 53
2] 52.65
3] 51.84
4] 60.09

42. Mohan deposits Rs.150 on the first of every month starting from 1st Jan1985, in the recurring deposit scheme of a bank which allows simple interest @ 6% p.a.on the sum standing to his credit at the end of each month. What is the amount, Mohan is entitled to on 31st Dec, 1985

1] Rs.1818
2] Rs.1800
3] Rs.1450
4] Rs.1400.80

43. A strip of paper 100m long, 4cm wide and 0.1mm thick is wound round a cylindrical
Core of diameter 10 cm and height 4cm. What is the diameter of the cylinder now?
1] 41.2cm2           2] 40cm3             3] 43.5cm              4] 63cm

44. A rhombus has sides 10cm each and the circle that is inscribed in it has radius 1.5cm.
What is the area of the rhombus in cm2

1] 30cm2           2] 15cm2             3] 4cm2             4] 10cm2

45. To comfortably sit in a room, every girl must be allowed a floor space of 2 sq.m. and air space of 5.5 cubic metres. Fifty girls are to be seated comfortably in a room 10m. long. What should be its height?

1] 5.5m          2] 6.6m           3] 6.5m          4] 5m

46. Simplify sqrt(64+64x2) = sqrt(25+25x2)

1] 3sqrt(1+x2)             2] sqrt(1+x2)               3] sqrt(1-x2)                 4] 4sqrt(x2)

47. O is the centre of a circle. XP is a tangent at X.Angel YXP = 50o. Find the measure of the arc XYZ

1] 100o         2] 50o            3] 180o             4] 90o

48. Two positive numbers are such that the ratio of the square of the first to the cube of the second is to the ratio of the cube of the first to the square of the second as 1/20. Find the ratio of the 2 numbers.

1] 3:4        2] 2:1          3] 1:2            4] cannot be determind.

49. Company A pays 5.5% on shares of Rs.100, and another pays at the rate of 3.5%
On shares of Rs.10 each. If the price of the former be Rs.150.00 and of the later Rs.15.00, compare the rates of interest which the shares return to a purchaser.

1] 36.67% and 86.37%                         2] 37.66% and 86.66%
3] 67.36% and 87.36%                          4] None of these.

50. Factorise(x-y)3+(y-z)3-(x-z)3
1] 3(x-y)(y-z)(x-z)                        2] 3(xyz)
3] 3x-3y-3z                                  4] cannot be found.

QUANTITATIVE APTITUDE TEST PAPER 3 : EXPLANATORY ANSWERS

--------------------------------------------------------------------------------

1. A = 50pts., B = 40pts.
B = 50pts., C = 30pts.
l.c.m. of 50 and 40 is 200
If B gets 200, A gets 250, C gets 150pts.
If A gets 50, C gets 50*150/250 = 30pts.
Hence[1]

2. Work done by x and y in 5 min = 5(10+15/150) = 5/6
Remaining work = 1/6
for doing 1/15 work, q takes 1 min.
for doing 1/6 work,?
1/6*1*15 = 5/2 min
Hence [4]

3. Let time be t and speed be s.
Distance travelled = st = 2/3 s*(t+2)
t = 2/3 (t+2)
t = 4hrs.
Hence [2]

4. Let the speed be x.
When speed becomes 3/4th of the usual time, time becomes 4/3 i.e. 1/3rd more of the usual
time.
1/3rd of usual time = 45min.
1/3rd of usual time taken to travel by = 45-15
1/3rd of usual time taken to travel AB = 10kms = 15min.
Usual time taken to travel 10km = 45 min
usual speed = 10*60/45 = 40/3 km/hr
Usual time taken to travel Ay = 45*3 =135 min = 2 hrs.15min.
Distance = 40/3*135/60 = 90/3 = 30 km
Total distance = 30+30 = 60km
Hence[1]

5. 12km/hr = 12*100/60 = 200metres/min
Distance of the cat from the rat = 50+200 = 250metres
Since both are moving in same direction, the rat gains 15-12 = 3km/hr i.e. 50 metres/min
Time required to overtake = 250/50 = 5 min
Hence [1]

6. Let time be t hrs after 5a.m.
6.5t-5 = 30
6.5t = 35
t = 5 1/3 hrs.
The resoirvoir will fill at 5a.m.+5 hrs20min = 10.20a.m.
Hence[3]

7. speed down the river = 5km/hr
speed up the river = 5/(1 1/3) = 3.75 km/hr
speed of the current = 1/2(5-3.75) = 0.625 km/hr
Hence[1]

8. 15m + 10b = 12m+20b
3m = 10b
money earned by 10 boys = Rs.100
Rs.100 = money earned by 3 men.
1 man should be paid 100/3 = Rs.33.33
Hence[2]

9.The cop gains 1/8-1/12 = 1/24 km/min = 41 2/3 m/min
To gain 100m, time, 100/(41 2/3) = 2.4 min
The thief has gone ahead by 2.4*1/12*1000 = 200m
Hence [1]

10. If the sides are 5x, 6x and 7x
s = 18x/2 = 9x
Area = sqrt[s(s-a)(s-b)(s-c)] = 800
= sqrt[9x(9x-5x)(9x-6x)(9x-7x)] = 800
x = sqrt[800/sqrt(216)]
Hence [2]

11. s = a+b+c+d/2 = 50/2 = 25
Area of the quadrilateral = sqrt(10*13*15*12) = 30*sqrt(26)cm2
Hence [1]

12. Area of 4 walls = perimeter*height
= 2(40+15)*h
= 110*h
Area = 7500/5 = 1500
1500 = 110h
h = 13.63
Hence[2]

13. Area = 1/2(sum of parallel sides * height)
= 1/2 * sum of sides *20
800 = 10*sum of parallel sides
80 = sum of parallel sides
x + (x+10) = 80
x = 35
other side = 45
Hence[1]

14. 450/200
200r = 900
r = 4.5 cm
Hence[4]

15 . density of steel is 1 i.e. iron is 8
weight of iron ball = weight of steel
volume of iron *8 = volume of steel *1
r3*8 = 512
r3= 512/8 = 64
r = 4
diameter = 8
Hence[4]

16. sc = 2*22/7*r*h = 2*22/7*5*3 = 30*22/7 cm2
volume = 22/7*r*r*h = 75*22/7 cm2
Hence [4]

17. New volume/old volume = (22/7*49*r*r*h)/(22/7*r*r*25*h) = 49/25
If old is 25, new is 49, then increase is 24
increase% = 24/25*100 = 96%
Hence[2]

18. Length of water column = 6000/60
volume of water = 100*10*200 = 2*105m3
weight of water = 2*105*1000kgs
= 2*105 tons
Hence[3]

19. Length of water column = 6000/60 = 100m/min
volume of water = 100*10*200 = 2*10 5m3
Weight of water = 2*105*1000kgs
= 2*105 tons
Hence[3]

20. Total surface area of a cylinder = 2*22/7*r*h+2*22/7*r*r
= 2*22/7*7*10+2*22/7*7*7
= 440+308
= 748
Hence[1]

21. 2*22/7*r*h
= 2*22/7*2*20
= 80*22/7
Hence[2]

22. r+h = 40
2*22/7*r*r+2*22/7*r*h = 2*22/7*r(r+h)
2*22/7*r(r+h) = 1760
r = 7
h = 33
volume = 22/7*r*r*h = 22/7*7*7*33 = 5082 m3
Hence[3]

23. Let 3r,4r be the radii
Let 2h, 3h be the height.
Ratio of volumes = 1/2
Hence [1]

24. Let heights = h,2h
Let radii be r and R
22/7*r*r*h = 2*22/7*R*R*h
r*r = 2(R*R)
r/R = sqrt(2)/1
Hence[3]

25. Let correct time be x.
distance travelled in (x+10) min. at 20km/hr
Distance travelled in (x+2) at 30km/hr
(x+10)*20/60 = (x+2))*30/60
x = 14 min.
Hence [3]

26. x/20-x/40 = 6
2x-x/40 = 6x = 240km
Hence[2]

27. Let speed be x.
360/x - 360/(x+20) = 3
360(x+20)-360x = 3x(x+20)
(x+60)(x-40)
x = 40
Hence [1]

28. Suppose the first distance is covered in x hours and 2nd distance in y hours.
4x+6y = 30
6x+4y = 32
Solving equations,
x = 3.6 hrs.,y = 2.6 hrs.
Total time = 6.2 hrs.
Hence[2]

29. Distance covered by thief in 1hr. is 20km.
Now 10 km will be compensated in 1 hr.,
20 km will be compensated in 2 hrs.
So, he overtakes the thief at 4p.m.
Hence[3]

30. 1/2:1/3 = 3:2
If y takes 2 min., x takes 3 mins.
If y takes 24 min, x takes 24*3/2 = 36 min.
Hence[4]

31. -19,-17, -13,-11,-7

32. +1,-3

33. *2.5, *3.5, *4.5, *5.5, *6.5

34. +7,*7

35. Area of circle = 22/7*r*r = 22/7*21*21 = 1386
Area of triangle = 1/2 b*h

36. no exp

37.+88, -143

38. 7695/855=9, 69255/7695=9, .....5609655/623295=9

39. Weight of jar = w1g
Weight of liquid = w2-w
Weight of liquid(half filled with liquid) = w2-w1
Weight of liquid filled = 2(w2-w1)
Weight of jar + weight of liquid = w1+2(w2-w1)
= 2w2-w1
Hence [3]

40. In finding average speed, we use Harmonic mean.
H.M.= 1/{1/3[1/x+1/2x+1/3x]}= 18x/11 km/hr.
Hence[4]

41. Draw XE to YZ
By pythagoras theorem,
(XE) 2= (XY) 2-(YE) 2= (15) 2-(9) 2 =144
Let AB = CD = x.
AD/XE = AY/EY
x = 71/5
x2= 51.84
Hence [3]

42. Total money deposited = Rs.12*150 = Rs.1800
Interest on Rs.150 for 12 months = 150*12/12*6*1/100 = 9
Interest on Rs.150 for 11 months = 150*11/12*6*1/100 = 33/4
Interest on Rs.150 for 1 month = 150*1/12*6*1/100 = 3/4
Total interest = 9/1+33/4+3/4 = Rs.18
Total amount due = 1800+18 = Rs.1818
Hence [3]

43. Volume of core = 22/7*10/4*10/4*4cm3
Volume of core with paper = 22/7*d/4*d/4*4cm3
Volume of paper alone = 22/7[d2/16-102/16]*4cm2
= 22/7*[d2-100/4]cm3
Also, volume of paper = 22/7*100*100*4*0.1/10cm3
= 100*22/7*400*0.1/10cm3
= 400cm3
400*22/7 = 22/7(d2-100)/4
d2 = sqrt(1700) = 41.2(approx)
Hence[1]

44. Total are = 4 area(triangleOAB)
= 4*1/2*10*1.5 = 30cm2
Hence[1]

45. floor space required = 100m2
Air space required = 100*5.5m3 = 550m3
Height = 550/100 = 5.5m
Hence[1]

46. 64+64x2 = 64(1+x2)
25+25x2 = 25(1+x2)
sqrt(64+64x2)-sqrt(25+25x2) = 8sqrt(1+x2)-5sqrt(1+x2)
= 3sqrt(1.x2)
Hence [1]

47. Measure of arc XYZ = XOY
= 2(XDY)
=2(XYP)
=2*50o = 100o
Hence [1]

48. Let the two no.s be x and y.
(x2/y3)/(x3/y2) = 1/20
x2/y3*y2/x3 = 1/20
1/xy = 1/20
We cannot find x:y
Hence[4]

49. 1st investment = An investment of Rs.150 fetches a dividend of Rs.5.50
Rate = 5.50/150*100 = 36.67%(approx)
2nd investment = An investment of Rs.15 fetches a dividend of Rs.0.35
Rate = 0.35/15*100 = 86.37%(approx)
Hence[1]

50. If a+b+c = 0, then a3+b3+c3 = 3abc
Putting x-y = a,y-z = b, x-z = c
Then a+b+c = 0
The factors are 3(x-y)(y-z)(x-z)
Hence[1]

Aptitude 3

1. Suman borrowed Rs. 60,000 to build a bungalow. She pays 10 % S.I. She lets out her bungalow and receives a rent of Rs. 1500 p.m. In how many years will she clear her debt.

    1 year     4 years    5 years     2 years

2. If the interest on Rs. 800 exceeds that on Rs. 600 by Rs. 15.50 in 6 months, find the rate percent p.a.

    15 I/2 %     18 1/2 %     14%     5%

3. Find the compound interest in Rs.2400 for 2 1/2 years at 5 % p.a.,interest being compounded annually.

    270.50     300     412.25     312.15

4. A square piece of ground is 45 metres long. Find the cost of fencing it round with 10 lines of wire at the rate of Rs. 1.50 per metre.
    2700     2500     2300     2800

5. The external dimensions of a box are 10 cm , 6 cm , & 4 cm. If the thickness of wood is 1 cm, Find the volume of wood.
    125     150     176     183

6. The radii of two cylinders are in the ratio 2 : 3 and heights 5 : 3. Calculate ratio of their volumes.
    20 /27     27/ 20    3 /4     20 /32

7. The diameter of a roller. 100 cm long is 60 cm. It takes 500 complete revolutions to level a playground. What is the cost of levelling @ 50 ps. per sq. m.
    Rs. 200      Rs. 220      Rs.400      Rs. 500

8. If a+b+c = 0.The value of
a4+b4+c4/b2c2+c2a2+a2b2 is :
    2     3     6     8

9. A man divides his property among his sons so that one gets half, another gets quarter and third gets one fifth and the fourth Rs. 10000. What is the value of the total property?
    200000     400000     1400000     2400000

10. If m:n = 2:3, the value of 3m+5n/6m-n is
    7/3     3/7     5/3     3/5

11. Divide 27 into two parts so that 5 times the first and eleven times the second are together equal to 195
    17:10     15:11     16:10     10:17

12. 40% of 5/6 is
    1/3     2/3     2/6     3/4

13. A dog taken 4 leaps for every 5 leaps of a hare but three leaps of the dog is equal to 4 leaps of the hare. Compare their speeds.
    16:15      12:16      19:20      10:12

14. 55 men can finish a job in 42 days. If the work has to be completed 9 days earlier, how many additional men must be engaged to complete the work?
    15     20     25     12

15. A retailer buys an electronic buzzer for Rs. 215. His overhead expenses are Rs. 25. If he sells the buzzer for Rs. 300, his profit percentage would be
    25%     26%     20%     30%

16. In an election between two candidates one got 55% of the total valid votes. 20% of the votes are invalid. If the total votes are 7500, what is the number of valid votes that the other person got?
    2700     2800     3000     3300

17. Aunt uses a car to travel from mumbai to nashik. She travelled at 60 kmph and covered half the distance in 2 hours. At what uniform speed should she travel to reach nashik at 4.00 pm?
    40     60     50     35

18. The sum of ages of Nitya and her aunt is 63 years. Four years ago her aunt's age was 4 times that of Nitya's ages at that time. What is the present age in years of Nitya's aunt?
    48     50     45     40

19. A watch ticks 90 times in 95 secs. And another watch ticks 315 times in 323 secs. If they start together, how many times will they tick together in first hour?
    101 times      100 times      99 times      102 times

20. Area of a square is given to be S. If the sides are doubled, then the new area will be,
    4S     2S     S/2     S2

21. The product of two numbers is 2400. If the bigger number is 1.5 times the smaller number is
    40     45     35     30

22. Six men earn as much as 8 women, 2 women earn as much as 3 boys and 4 boys earn as much as 5 girls. If a girl earn Rs.50 a day, then the earning of a man would be
    Rs.125      Rs.135      Rs.105      Rs.120

23. A train 150 meters long running at a speed of 60 kmph takes 30 seconds to cross a bridge. The length of the bridge is,
    350m     450m     300m     400m

24. If a sum of money at certain rate of interest doubles in 5 years and at a different rate of interest becomes 3 times in 12 years, the better rate of interest is,
    20%     10%     162/3     15%

25. 126, 756,252,1512, ____
    504    500    1210    None of these

26. The cost of painting the walls of a hall 30 meters long, 20 meters broad and 12 meters high, if it costs 25 paise per sq. metre.
    Rs.300      Rs.325      Rs.350      Rs.400

27. The product of 3sqrt(4), 6sqrt(6) and 2sqrt(5) is
    6sqrt(12000)      6sqrt(1000)      4sqrt(12000)      3sqrt(120000)

28. If A can complete a work in 6 hours, and B can complete it in 8 hours, then how much time would they take to complete the work together?
    3 3/7     2 5/2     4 5/6     none of these.

29. A,B,and C can independently complete a task in 6,8 and 12 hours respectively. C starts working. 2 hours later she stops and simultaneously A and B starts working. Yet another 2 hours later, B stops working too. Now how long does A have to work alone to complete the task?
    2 hours      1.5 hours      3 hours      4 hours

30. 128, 32, 224, 56, ____
    392     350     25     36

31. Taps A and B can independently fill a tank in 6 and 10 hours . Leak C can empty a filled tank in 8 hours. On an empty tank A, B, C are opened. How long does it take to fill the tank?
    7.05     8.05     10.10    5.07

32. Ten years age, Ram was 2/3 Shyam's age. 10 years hence Shyam will be 25% older than Ram. What are their present ages?
    30;40     40;30     20;40     30;60

33. 25 years ago A's age was 1/3 of what B's age will be 25 years hence 50 years hence, B's age will be twice A's present age. What is the sum of their present ages?
    90     100     200     400

34. The sum of X and Y's age is 105. When X was Y's age, she was 1.5 times Y's age then what are their present ages?
    45;60     30;40     50;60     60;45

35. 10 men working for 20 days, 5 hours a day can build a fence of length 20 meters. I need to build a fence of length 100 metres in 5 days and the men are willing to work 10 hours a day. How many men do we need?
    200     300     400     100

36. Find the factor of a4+64
    (a2+8)(a2-8)      (a2+2)(a2-2)      (a2+4a+8)(a2-4a+8)      none of these.

37. A contractor undertakes to complete a project in 56 days using 100 men. However after 46 days, 100 men thereby completing the project on time. Had the additional men not been deployed, then by how many days would the project be delayed?
    10     20     5     40

38. Exam-1 = 30/50 Exam2 = 40/50
a) what is the increase in percent?
b) What is the % of increase?
    20;33 1/3      33 1/3;20      20;40      40;33 1/3

39. a) What is 30% of 60%?
b) What % is 30% of 60%?
c) What % of 30% is 60%?
    17%;45%;190% 18%;50%;200% 20%;100%;150% 50%;18%;200%

40. a)The price of sugar increases by 25%. By what % should consumption be decreased so that expenditure on sugar remains constant?
b)Consider the same problem but price increases by 50%?
    40;66.66      80;99.99      20;33.33      10;11.11

41. I have bought a car for some amount. I sell it to Mr.X at 10% loss due to need of money urgently. But later I buy it again from him at my original purchase price.
a)What is Mr.X's profit?
b)What is my loss?
    11.11%;10%      10%;11.11%      20%;22.22%      40%;44.44%

42. A farmer purchases 2 horses for the same price. One he sells at a 10% profit and the other he sells at a 10% loss. What is his overall profit or loss?
    Rs.200 loss      Rs.200 profit      no loss,no profit      Rs.400 loss

43. A farmer sells 2 horses for the same price. In one he gains 20% and in the other he loses 20%. What is his overall profit or loss?
    4% profit      4% loss      2% loss      2% profit

44. Money doubles in 3 years. When does it become 8 times?
    24 years      12 years      6 years      18 years

45. A magician can double the no. of coins given to her in 1 minute. I give her a certain no. of coins and after an hour she has a boxfull of coins. When was the box 1/4 filled?
    15 min      30 min      58 min      45 min

46. Principal Rs. 100, rate of interest 10%, compound interest, duration 2 years.
a)Compounded annually
c)Compounded daily
    121     120     100     12.1

47. I buy a 20% stock of face value 50/- at 45/- and sell it at 55/-. A year later, what is my yield?
    45.44%      44.45%      54.55%      55.54%

48. A dishonest seller pretends to sell his goods at cost price, but he uses a weight of 950gm for the kg weight. Find his gain%
    5     6     7     4.5

49. P lent Rs.600 to Q for 2 years and Rs.150 to R for 4 years and received altogether from both Rs.90 as interest. Find the rate of interest, simple interest being calculated.
    1%     5%     6%    3.5%

50. P owes Q Rs.455 payable 4 months hence and Q owes P Rs.450 payable 2 months hence. If they agree to settle their account what sum should be paid over and to whom reckoning the rate of true discount p.a.
    Rs.12      Rs.13   Rs.11     Rs.16

QUANTITATIVE APTITUDE TEST PAPER 2 : EXPLANATORY ANSWERS

--------------------------------------------------------------------------------

1. S.I = 60,000 * 10 /100
= Rs. 6000
Rent received = 1500 * 12
= 18000
Therefore debt cleared in one year = 18000 - 6000
=12000
Therefore in 5 years.

2. 800 - 600 = 200
n = 6 months. = 1 /2 year
r = 100 I /Pn
= 100 * 15.50/ 200 * 1/2
= 1550 / 100
= 15.5%

3. A = P ( 1 + r/ 1002 ( 1 + r /100)
= 2400 ( 1+ 5 /1002 ( 1 + 2 1/2/100)
= Rs. 2712.15
Therefore C. I. = 2712.15 -150; 2400
= Rs. 312.15

4. Perimeter of square = 4a = 4 * 45
=180 m
Length of fence = 10 * 180
=1800m. with 10 lines of wire.
Therefore cost of wire = 1.50 * 1800
= Rs. 2700

5. External volume = l * b * h
= 10 * 6 * 4
= 240 cm3
Internal dimensions = ( 10 -2); ( 6- 2); ( 4- 2)
= 8 , 4 , 2 cm.
Internal volume = 8 * 4 * 2
= 64 cm3
Therefore volume of cube = 240 - 64
= 176 cm3

6. Let radii --> 2x and 3x
Let height --> 5y and 3y
V1 /V 2= ( 22 /7 ) ( 2x ) 2 ( 5 y ) / ( 22 /7 ) ( 3x ) 2 ( 3y )
= 20 / 27

7. Diameter of a roller = 60 cm
r = 30 cm = 0.30 m
Height of roller = 1.00 m
Curved surface area = 2 ( 22 / 7 ) rh
= 2 * ( 22 / 7 ) * 0.30 * 1
= 1.32 / 7
= 0.88
Area covered by roller = 500 * 0.88
= 88 * 5
= 440 cm2
Therefore cost of levelling = 0.50 * 440
=5 * 44
= 220

8. Since a+b+c = 0
a+b = -c
(a+b2=(-c2)
a2+2ab+b2=c2
a2+b2-c2= -2ab
(a2+b2+c2) 2=(-2ab) 2
or
a4+b4+c4+2a2b2-2b2c2-2c
2a2=4a2b2
or
a4+b4+c4=2a2b2+2b2c2+2c2a2
or
=2(a2b2+b2c2+c2a2)
a4+b4+c4/a2b2+b2c2+c2a2
= 2

9. Let x be the total value of the property.
x = x/2+x/4+1/5x+10000
= (10+5+4)x/20+10000
= 19x/20+10000
= 20*10000
= 200000

10. m/n = 2/3
3m = 2n
now, 3m+5n/6m-n = 2n+5n/4n-n = 7n/3n = 7/3

11. a+b = 27
5a+11b = 195
solving simultaneously we have,
a = 17 b = 10

12. 40% of 5/6 = 40/100*5/6 = 1/3

13. 3 leaps of the dog = 4 leaps of the hare.
1 leap of the dog = 4/3 leaps of the hare.
4 leaps of the dog = 16/3 leaps of the hare.
Speed of the dog : Speed of the hare
16: 15

14. 9 days earlier mean that the work should be completed in (42-9) = 33 days.
No. of Men = 42*55/33 = 70
Hence the no. of extra men = 70-55
=15 men

15. Total cost of the electronic buzzer = Rs.215+Rs.25 = Rs.240
Selling Price = Rs.300
Profit% = 60/240*100 = 25%

16. 7500*20%=1500
No of valid votes=6000
45% of 6000=2700
Hence[1]

17. At the speed of 60 kmph, aunt will reach nashik in 4 hours.
The distance between mumbai and nashik is 240 kms.
If 120 km are to be covered in 3 hours then aunt should travel at the uniform speed of
120/3 = 40kmph

18. If x and y are the ages of Nitya and Nitya's aunt,
x+y = 63
y-x = 4(x-4)
we have Nitya's age = 15 years
her aunt's age = 48 years

19. First watch ticks after 95/90 seconds.
second watch after 323/315 seconds.
LCM = 19*5*17/45 seconds.
No. of times they will tick in first 3600 seconds = 3600/(19*5*17)/45
Once they have ticked together in the begining , 50 in 1 hour they tick 100+1 = 101 times

20. If area = S, Sides = sqrt(S)
If side is doubled i.e. 2sqrt(S)
area = {2sqrt(S)}2
= 4S

21. Let a and b be the numbers where b is the bigger number.
b =3/2a
a-b = 2400(given)
3/2a2= 2400
a2= 1600
a = 40

22. 6 M = 8W, 2W = 3B, 4B = 5G
1 G = Rs. 50 a day.
Now, 1B = 5/4G 1 W = 3/2 * 5/4G
1 M= 8/6* 3/2* 5/4G = 5/2G
1 M = 5/2 * 50 = 125/-Rs.

23. The distance covered by the train in 30 seconds = 6000/3600* 30 metres
= 500 metres.
Length of the Bridge = 500 - 150
= 350m.

24. If we assume that the sum = Rs. 100
Then, 1st rate of interest = 100*100/100*5 = 20
2nd rate of interest = 200*100/100*12 = 16 2/3
76n1=5, x1= 42.2 n2 = 4, x2 = 35.5
x12 = n1x1+ n2x2 / n1+n2
= 5 * 42.2 + 4 * 35.5 /9
= 211.0 + 142.0 /9
= 353 /9
= 39 2/9

25.*6, /3
Hence[1]

26. Area of the four walls.
= 2(length + breadth ) * height
= 2 (30 + 20 ) *12 sq. meteres
= 1200 sq. metres
Total cost of painting = Rs. 1200*25/100
= Rs.300

27.Product of 3 sqrt (4), 6 sqrt (6), 2 sqrt (5) is
4 1/3 * 6 1/6 *5 1/2
=42/6 * 61/6 * 53/6=(42 * 6 * 53)1/6
=( 16 *6 *125)1/6
= 6 sqrt.12000

28. A takes 6 hours to complete a work.
He can complete 1/6th of the work in one hour.(taking complete work as 1.)
B takes 8 hours to complete it.
He can complete 1/8th of the work in one hour.
Together, A and B can complete,
1/6+1/8 = 14/48 = 7/24 of the work.
Hour     Work
1           7/24

?            24/24

=24/7 = 3 3/7
Hence, [1]

29. In one hour, C can complete 1/12th of the work.
In two hours, he can complete 1/12*2 = 2/12th of the work.
A and B start work simultaneously,
together work completed by A and B,
1/6+1/8 = 14/48 work = 7/24 work.
In 2 hours they complete 7/24*2 = 7/12 work
Total work done by A,B,C = 7/12+2/12 = 9/12
Total work to be completed = 12/12 or 1
Remaining work = 3/12
Hour       work done by A
1                           1/6

?                           3/12

3/12*6 = 1.5 hours
Hence[2]

30./4, *7
Hence[1]

31. In 1 hour C can empty 1/8th of tank
In 1 hour amount of water filled in the tank = A+B-C
= 1/6+1/10-1/8
68/480 = 17/120
Hour                Water filled in tank
1                                    17/120
?                                  120/120

= 120/17 = 7.05 hours

32. Let the present ages of Ram and Shyam be R and S resp.
3R-2S = 10 -- I
4S-5R = 10 -- II
15R-10S = 50
-15R+12S = 30
2S = 80
S = 40
R = 30
Hence,[1]

33. Let their present ages be A and B.
3A-B = 100 -- I
2A-B = 50 -- II
3A-B = 100
-2A-B = 50
A = 50
B = 50
Sum of their ages = A+B
=100
Hence[2]

34. Let their present ages be X and Y.
X+Y = 105 --I
1.5X-2Y = 0 --II
X = 60
Y = 45
Hence[4]

35.               M      D     H     L
old               10      20     5     20
new               x       5     10     100
10/x = 5/20*10/5*20/100
x = 100

36. a4+b4 = (a2+ab+b2)(a2-ab+b2)
=(a2+4a+8)(a2-4a+8)
=(a2+8)2-(4a)2
=a2+64
Hence[3]

37. x = 10*2 = 20 days
100 men would require 20 days from 46 days
46+20 = 66 days
But we want to complete the work in 56 days.
Hence[1]

38. Exam 1 = 30/50*100 = 60%
Exam 2 = 40/50*100 = 80%
Increase in percent =20%
percent in increase = 20/60*100 = 33 1/3%

39. a)30/100*60/100 = 18/100 = 18%
b)30% is 50% of 60%
c)60% is 200% of 30%

40. a)Old price of sugar = Rs.10/-
New price of sugar = Rs.12.5/-
Old consumption = (10*100) = 1000
New consumption = (12.5*x)= 1000
x = 1000/12.5 = Rs.80/-
Decrease in consumption = 20/100*100 = 20%

b) old price = Rs.10
New price=Rs.15
10*100 = 1000
15*x = 1000
x = 1000/15 = 66.66Rs.
Decrease in consumption = 33.33%

41. a)Let my cost price be 100
Selling price = 90
Profit for Mr. X = 10
Profit % = 10/90*100 = 11.11%
b) Let cost price be 100
Selling Price = 900
My loss = 10 = 10/100*100 = 10%

42. Let cost price be 100 of both horses.
horse1 = S.P. = 110
horse 2 = S.P.= 90
Total cost price = 100+100=200
total selling price= 110+90 = 200
Hence[3]

43. Horse 1-   C.P             S.P.
                        x               100
                        ?               120
S.P. = C.P.(100+profit%/100)
x = 83.33
Horse 2-          C.P              S.P.
                          y               100
                          ?                 80
y = 125
Total cost price = cost price of Horse1+cost price of Horse2
= 125 + 83.33 = 208.33
Total S.P.= 100+100 = 200
loss = 8.33
% of loss = 4%
Hence[2]

44. 3 years - 2 times
6 years - 4 times
9 years - 6 times
12 years - 8 times

45. In 60 min - box is full.
In 59 min - box is half filled.
In 58 min - box is 1/4 filled.
hence[3]

                                    2
46. A = 100(1+10/100)
= 100(110/100*110/100)
= 121

47 . Income = Rs.10/-
20%*50 = 10
capital gain = 55-45 = 10
gain = 10+10 = 20
% gain = 20/45*100 = 44.45%

48. Suppose goods cost him Rs.1/kg, then he sells goods costing Rs. 0.95 for Rs.1/-
gain = 1-0.95 = 0.05
% gain = 0.05/0.95*100 = 500/95 = 5%
Hence[1]

49. Let r be the rate of interest.
600*2*r/100 + 150*4*r/100 = 90
1200r/100 + 600r/100 = 90
r = 5
Hence[2]

50. p = Rs.455, n = 4months = 1/3 year, rate = 5%
Amount of Rs.100 = (455*1/3*5)/100 = 107.58
455                   ?
107.58             100
= 423
q = Rs.450, n = 2months = 1/6 year, rate = 5%
Amount of Rs.100 = (450*1/6*5)/100 = 103.75
450                      ?
103.75             100
= 434
Sum to be repaid to p = 434-423 = Rs.11
Hence [3]

Aptitude 2

If an article cost 50% of its selling price there was a profit of Rs60. What was the selling price?

125              120               140            200

A can do a piece of work in 10 days which can be done by B in 12 days. How long would it take to do the work together?

4 7/9         5 3/9            5 5/11         5 ½

The denominator of a fraction is greater than its numerator by 5 but if 7 were added to the denominator the value of the fraction would then become 1/4th . What is the fraction?

4/9             2/3               5/11            4/7

The sum of all 2 digit numbers which can be formed from 4 & 5 ?

45                99               100               101

Find the number whose double is greater than its half by 30.

20                 30              25                   23

A divided Rs. 200 amongst 15 children giving some Rs. 20 and remaining Rs.10.How many children receive Rs. 20?

7                  12                10                 5

If 3 apples are worth 2 bananas, how many bananas are 15 apples worth?

15               8                     10                   12

A buys an item for Rs. 600 of which 12% is excise and 4% is sales tax . How much would A pay exclusive of taxes and excise?

519.82     521.33        517.24           518.00

X has Rs. 6 with him. If 2/3 of what X has is ¼ of what Y has. How much does Y have?

8                 16                 12                      14

The sum of a number and its reciprocal is ½ . The sum of their squares is,

9/4            4/5             5/3                   7/4

X,Y,and Z take 20, 30 and 60 days respectively to complete a job independently. They set out to complete a job together . However Y leaves after 4 days and Z leaves after another 6 days . How many more days will it take for X alone to complete the job now?

4                 3                    5                         6

A rectangular block of dimensions 5*6*7 cm. Is dropped into a cylindrical vesssed of radius 6 cm. And height 10 cm.. If the level of fluid in the cylinder rises by 4 cm. , what portion of the block is immersed in the fluid?

22/7*15/18          22/7*24/35            22/7*22/34         22/7*12/15

The difference between a number and its square is 870. What is the number?

42              29                 30                      32

In an election , 60% of the voters exercised the franchise. Of these, 40% were women. The number of males exercising their franchise was 53040. How many eligible voters were there in all?

125000    150000    230000        153000

If the side of a square is increased by 3 cm., the area increases by 33 cm. The side of the square is

5.5             6                    2                      4

A sum of RS. 88000 is to be divided among A, B, and C such that for every rupee, A gets, B gets 75 paise and for every rupee, B gets , C gets 90 paise . How much is C’s share?

28345     28563        29887          30500

A family uses a mixture of a blend of 2 coffees costing Rs. 30 and Rs. 60 respectively.If the family uses only the expensive variety, it will have to spend Rs.450 more. The annual consumption of coffee of the family is 20Kgs. In what ratio are the two blends being used?

3:1             2:3               4:5                    2:1

A buys a washing machine costing Rs.6000 on instalment basis. He pays Rs. 3000 cash at the time of delivery and subsequently 2 monthly instalments of Rs. 1575 each. The rate of interest charged p.a. is

39%         32%             28%                 30%

If 4-[2.8-{3.5-(1-X)}]=5, Then value of X is

2.3           1.5               1.3                   2.5

A salesman earns a commission of 3% on the value of sale that he makes. If by selling a radio at 60 % of the marked prices, he earns a commission of Rs. 12, then the marked price of the radio is?
667            700              655           680

P, Q, and R enter into a Partnership and their shares are in proportion of 3:2:1.
P withdraws half his capital at the end of 4 months and after 8 months more the profit of Rs. 1800 is divided. What is P’s share
570             660              720             700

A sum of Rs. 8.25 is made up of 100 coins which are either 10 paise or 5 paise. How many are there of 10 paise?
65               35                 40                   55

A trader has 100 Kg of wheat, part of which he sells at 5% profit and the rest at 20% profit. He gains 15% on the whole. Find how much is sold at 5% profit?
60               50              66.6              33.3

If x*y*z = (x2+y2)z, then value of 4*3*2 is
650               675               550               625

If the side of a square is increased by 8cm, the area increases by 64cm2. What is the side of the square?
1.3                1.5                   1                 2

Ashish travels a distance of 100 km in the following manner, at 20 kmph for the 1st 50 kms, at 25 kmph for the next 50 kms. He returns at a constant speed of 25kmph. What was his average speed for the journey?
22.50          23.52          24.60         22.35

A purchases a car at a discount of 20% from a wholesaler and sells it at a profit of 20% for Rs.1800. How much discount did he get from the wholesaler?
60                85              70                 75

A radio can be brought for Rs.2000 cash or for Rs.2200 on 5 months credit. Find the interest rate p.a. Consider simple interest.
24               22                32                 25

If 20kg of rice cost Rs.200 less than 80 kgs of wheat. If a kg mixture of rice and wheat is in the proportion 2:3 and cost Rs.15, Find per kg cost of rice in Rs.
15               20          10            None of these.

X is 25% more efficient than Y and his hourly wages are 25% more. If X is paid Rs.75, how much will Y receive for the same work?
65            90             75          110

Ashish spends 10% of his pocket money on himself and gives his sister Rs.5. If he still has 80% of the original sum, what was the amount he had as pocket money?

A owes B a sum of Rs.5000 to be paid 6 months from today. If simple interest @12% p.a. is calculated, what sum shall A have to pay B, 4 months from now in full discharge of the debt?
4726      4824         4900         4906

The difference of 2 positive numbers is 81 and quotient obtained on dividing the one by the other is 9. Find the first number.
75           90                10             80

Anand goes to a shop to buy the walkman costing Rs.2250. The rate of sales tax is 6% he wants the dealer to reduce the price so that he has to pay Rs.2000 inclusive of tax. Find the reduction needed in the percent of the walkman.
15            16               17               18

P,Q, R enter a partnership where they invest Rs. 20000, Rs. 30000, Rs. 40000 resp. P withdraws Rs. 10000 after 2 months, Q withdraws Rs. 15000 after 4 months and R withdraws Rs. 25000 after 8 months. What will be R’s share in the profit of Rs. 12474? 3564         3267       5643               5500

A company declares a dividend of 15% on Rs.150 shares. A man buys such shares and gets 10% on his investment. Find at what price he bought the shares?
255           356            225            240

If x sells for Rs.20 each, 250 Rs.10 share in a company which pays a dividend of 10% and then invests the proceeds of this sale in the purchase of Rs.5 shares in another company at Rs.4 each, find what difference is made in his income if the company pays a dividend of 4%?
50            66              105               None of these.

¼ of one number + 2/3 of another = 3/8 of their sum. Find the ratio of their numbers.
4:3         2:5               3:7                 2:1

At how many distinct points do the diagonals of a square intersect if no 2 diagonals pass through the same point?
4              1                  2                      3

X buys an apple from Y for Rs.5 and sells it to Z for Rs.10. He later buys the apple back from Z for Rs.12 and sells it to Y for Rs.15. What is his profit over the venture?
8              6                         12                10

I have a rectangular piece of cloth 16 meters long & 1 1/4 metre broad. Iwant to cut as many large square pieces of the same size as possible. How many such pieces can I cut out of it ?
320          240                   360               325

The sum of two natural numbers is 85 and their L . C .M is 102. Find the numbers
51 & 34                25&63                    40&25

A man XY of height 1.75 cm stands at a distance of 4 metres from a pillar AB. If the pillar
l is at the height of 5.25 m from the ground, what is the length of the man's shadow on the ground ?
1m           2m                   5m                 6m

triangles x & y have the same area. If the bases are in the ratio 2 : 3, what is the ratio of their heights ?
3:2             2:3                 3:4                    5:6

A ground of 4.9 m width is prepared on the inside of a circular area of diameter 10 m. Find the cost of levelling the garden at Rs. 10 per sqm.
789.25     653.43         775.54            650.33

Three circloes touch each other externally. If xy = 15 ,yz = 10, xz = 21 Find the radius of each circle.
13 ,8 ,2     14 , 5 ,9        10 ,13 ,12         5 ,6 ,3

If the diameter of a circle is increased by 100 %, find the % increase in the area.
200           300                 100                   250

A spherical ball of 8 cm diameter is melted into a cone with base 20 cm in diameter. Find its height.
2.56cm     3 cm              2 cm                 3.75 cm

Water flows out at the rate of 10m per minute, from a cylindrical pipe of diameter 5
mm. Find the time taken to fill a conical tank whose diameter at the surface is 40 cm and
depth 24cm.
53 1/2 min           51 1/5 min            57 1/5 min       60 min

Find the S.I. for Rs.2500 for 73 days at 6 % p.a.
Rs.30                        2]Rs.50                        Rs.40                 Rs.20

QUANTITATIVE APTITUDE TEST PAPER 1 : EXPLANATORY ANSWERS

Let the selling price be S .

Cost price = C = 0.5S
Profit = 0.5S
0.5S = 60
S = 120

In one day A can do 1/1 work

In one day B can do 1/12 work
In one day A+B =1/10+1/12
=22/120 =11/60
=60/11 = 5 5/11

Let the fraction be a/b

b = a+5 --I
Also, a/b+7 =1/4
4a = b+7 --II
Solving I+II,
-a+b = 5
4a-b = 7
3a = 12
a = 4, therefore b = 9

45, 54

sum = 45+54 = 99

Let the number be x

2x-1/2x = 30
3/2x = 30
3x = 60
x = 20

6. 20x+10y = 200 --I
x+y = 15 --II
20x+10y =200
(-)10x+10y = 150
10x = 50
x = 5

7. Apples          Bananas
        3                 2
       15                     ?

15*2/3 = 10 Bananas

cost exclusive of excise and tax = x

excise = 0.12
Tax= 0.04
X+0.16x = 600
X = 600/1.16
= 517.24

x has Rs. 6.

2/3 of x = 2/3*6 = Rs. 4
Rs. 4 = ¼ y
Y = 4*4 = 16

x+1/x = ½
(x+1/x)2 = x2 + 2x1/x + 1/x2
= x2 +2 +1/x2
= x2 + 1/x2 + 2
= ¼+2
=1+8/4
= 9/4

x will complete 1/20 in one day.

Y will complete 1/30 in one day.
Z will complete 1/60 in one day.
4 days = (1/20 + 1/30 + 1/60)*4
= (3+2+1/60)*4
= 6/60*4
= 4/10
= 2/5th complete
6 days = (1/20 + 1/60)*6
= (3+1/60)*6
= 4/60*6
= 4/10 = 2/5
total work complete = 2/5+2/5 = 4/5
work remaining = 1/5
1/5/1/20=1/5*20/1
= 4 days

volume increase in cylinder=(volume of block *portion of it which is immersed)

22/7*62*4 = 5*6*7( p)
p = 22/7*36*4
           5*6*7

p = 22/7*24/35

Let the number be x.

X2-x = 870
X2-30x+29x-870 = 0
(x-30)(x+29) = 0
x = 30

Let the no. of eligible voters = x

Then, (0.6)(.6x) = 53040
0.36x = 53040
x = 54000/0.36
x = 150000

Let side of the square be x.

(x+3)2 = x2 + 33
x2+6x+9=x2+33
6x=24
x=4

A:B is 10:7.5

B:C is 10:9
A:B:C is 100:75:67.5
C gets 90*88000/242.5=24495

Expensive brand cost = 20*60=1200

Expense now = 1200-450=750
Average cost of the mixture =750/20
Rs.30 Rs. 60
Rs. 750/20
450/20 150/20
3:1

Instalments paid = 1575+1575 = 3150

Interest = 3150-3000 = 150
For 2 months interest = Rs.150
Rate of interest 2.5%p.m.
Rate of interest p.a. = 12*2.5 = 30%

4-2.8+3.5-1+x=5

x=5-4+2.8-3.5+1
=1.3

Let the marked price be 100.

Selling price =60
Commission = 3/100*60 = 1.8
Commission(%) Commission(Rs).
1.8                          12
100                           ?

100*12/1.8=666.67

         3:2:1

1.5*12+1.5*4:2*12:1*12
18+6:24:12
24:24:12
2:2:1
1800/5*2
360*2
Rs.720.

    By alligation rule:

10                                5

                       825/100

         13                                7

10 paise = 100/20*13
= 65 coins
5 paise =100/20*7
=35 coins

      23. By alligation rule:
           5                      20

                      15

           5                      10
       2/3*100=66.6

= (16+9)2

= 252
= 625

25. Let side be x.
(x+8)2 = x2+80
x2+16x+64=x2+80
16x=16
x=1

Total time taken = 2.5+2+4=8.5 hour

Distance = 100+100 = 200 kms
Speed = 200/8.5 = 23.52

     27. 120              1800
            100              ?
100/1800*120 = 1500
Cost price = 1500
100*1500/80 = 1875
Discount from the wholesaler= 20%*1875= Rs375

    28. 200/2000*12/5*100 = 24% p.a.

Let cost of rice be Rs.x per kg.

And cost of wheat be Rs.y per kg.
20x = 80y-200
x = 4y-10
x-4y = 10
2x-8y = 20 -- I
2x+3y/5 = 15
2x+3y = 75 --II
2x+3y = 75
-2x-8y = 20
5y = 55
y = 11
x-44 = 10
x = 54
2x-8y = 20
2x+3y= 75
-11y = -55
y = 5
x = 10

Let wages of y =a, then x=1.25a

X took 75/1.25a = 60/a
Y will take 1.25*60/a
=75/a*a
=Rs.75

Let his pocket money be x.

His expense = 10%
0.1x + 5 = 0.2x
5 = 0.1x
5/0.1=x
x = Rs. 50

Principal amount = x

5000 = x + x*6/12*12/100

5000 = x+3x/50
5000 = 50x+3x/50
250000 = 53x
x = 250000/53
Rs. 4717
4717*4/12*12/100
Rs. 189
Amount = 4717+189
Rs. 4906

Let the 2 no.s x and y.

x-y = 80 --I
x/y = 9 --II
x-y = 80
x-9y = 0
8y = 80
y = 10
x-y = 80
x-10 = 80
x = 90

2250*6% = 135

2250+135= 2385
2385-2000=Rs. 385
discount% = 385/2385*180
= 16.14%
Hence [2]

P      Q         R

2       3           4

1*12+1*10 1.5*4+1.5*12 2.5*8+1.5*12
22 6+18 20+18
22 24 38
11:12:19
P = 12474/42*11 = 3267
Q = 12474/42*12= 3564
R = 12474*19/42=5643

Dividend = 150*15% = 22.50

Let market value be x.
Rate of return on investment = 22.5/x*100
10x = 2250
x = 225

250 Rs.10 shares = Rs.2500

dividend = Rs.250
Proceeds of sale = 250*20 = Rs.5000
No. of Rs. 5 shares bought in the other company = 5000/4 = 1250
Capital = 1250*5 = 6250
Dividend in the other company = 6250*4%
= 250

Let numbers be x and y.

1/4x +2/3y = 3/8(x+y)
3x+8y/12 = 3x+3y/8
6x+16y = 9x+9y
7y = 3x
x:y = 3:7

39. The diagonals of a square intersect at 1 point if no 2 diagonals pass through the same point

40. cost price for x = 5
selling price for x = 10
profit = 5
cost price for x = 12
selling price = 15
profit = 3
total profit = 8

41. The H .C .F of 1600 and 125 is 25.
Length wise---- I can cut 64 breadthwise. 5 pieces
Altogether I can cut 320 pieces.

42. Let the numbers be H pH q Where H is their H. C. F. and p
q are prime to each other.
Then, their L.C. M = Hpq
Hp + Hq = 85 H pq = 102
Dividing , p + q / pq = 85 / 102 = 5 /6
Therefore the numbers p,q must be 3 2
H = 102 / 6 = 17
Therefore A = 17 * 3 = 51 B = 17 * 2 =34

43. Triangle SAB is similar to triangle SFL
SA / SF = AB / FL
x /x + 4 = 1.75 / 5.25 = 1/ 3
3x = x + 4
Therefore x = 2m

44. A ( triangle x) / A (triangle y) = b 1h 1 b 2h 2
b 1/ b 2 = 2 / 3
1 = 2 h1 / 3 h 2
Therefore h1/ h2 = 3 / 2

45. Area of the ground
( 22 /7 ) ( r 1 + r 2 ) ( r 2-150; r 2)
22 /7 * 5.1 * 4.9
= 77.54 sq.m
Cost of levelling. = 77.54 * 10
Rs. 775.54

46. r1 + r 2= 15
r 2 + r 3 = 10
r 1 + r 3= 21
2 ( r 1 + r 2+ r3 ) = 46
r 1+ r 2 + r 3 = 23
15 + r 3= 23
10 + r 1= 23
21 + r 2= 23
Therefore r 3= 8
R 1 = 13
R 2 = 2

47. When Diameter increased by 100 %
radius also increased by 100 %
Therefore radius = 2 r
Therefore original area of the circle / New area of the circle.
= ( 22 /7 ) r2/ ( 22 /7 ) ( 2 r2= ( 22 / 7) r2/ (22 /7) 4 r2= 1 /4
If the original area is 'A'
then new area = 4 A
increase in area = 4 A - A = 3A
Therefore % increase = 3 A / A * 100
= 300 %

48. Volume of cone = volume of sphere
1 / 3 ( 22/ 7) r2h
= 4 /3 ( 22 /7) r2
1 /3 * ( 22 / 7) * 102 h
= 4 /3 * ( 22 /7) * 43
102h= 256
100 h = 256
Therefore h = 2.56

49 . Volume of water flowing out in 1 minute.
= ( 22 /7) r2h
= ( 22/7) * 1/4 * 1/4 * 1000 c.c
Time taken = volume of conical tank / volume of water flowing out.
= 1 / 3 ( 22 /7) r2 h / (22 /7 ) r 2h
= 1 /3 * ( 22 / 7) * 20 * 20 * 24 / ( 22 / 7) * 1 /4 * 1/ 4 * 100
= 51 1/5 minutes.

50. S.I = 2500 * 73 / 365 * 6 / 100
= 30

Technical Concepts