XAT Aptitude-Numerical Contributed by Preethy updated on Mar 2019

XAT SECTION-3 Aptitude and numerical Previous Years Solved Question Papers

1. A spherical balloon is inflated and its radius is increasing at 4 cm/second. At what rate would the volume be increasing when its radius is 14cm?
(1) (56)3 cm3/sec
(3) 10,000cm3 /sec
(4) None of these

2. When (629)24 is divided by 21, find the remainder.
(2) 2
(3) 5
(4) 11

3 If a a/b b a a/b b , what set(s) of a and b is/are correct?

A. S1 = {a= any real value, b=0}
B. S2 = {a= 0, b= any real value}
C. S3 = {a= 0, b =0}
(1) Only A
(2) Only B
(3) Only A and B -Answer
(4) All A, B and C

4. Which of the following is the lowest?
(1) 302 –122 – 32 -Answer
(2) 352 –142 – 62
(3) 302 –102 - 53
(4) 332 –172 - 12

5. a, b and c are the sides of a triangle. Equations ax2 + bx + c = 0 and 3x2 + 4x + 5 = 0 have a common root. Then angle C is equal to
(1) 600
(3) 1200
(4) None of these

6. Sum of all prime numbers less than 50 is
(1) more than 500
(2) less than 200
(3) a prime number
(4) an even number-Answer

7. N = abc is a three-digit number, a, b and c being their respective digits. N is a perfect square of an even number. To find N which of following informations is/are necessary/ sufficient?
A. a, b, c are three consecutive digits but not in order. B.N is divisible by 18.
C. Units digit of N2 is c.
(1) Only A and B together are sufficient
(2) A and C together are sufficient
(3) Only B and C together are sufficient
(4) Either A and C together or B and C together are sufficient-Answer

8. Let x, y, z be three positive integers satisfying y = 3x, z = 4x, x + y + z = 3k, k is an integer.Which of the following is the smallest value of k for which x, y, z are even number?
(1) 8
(2) 10
(3) 12

9. N = aebfcg is a six- digit number where a, b, c, e, f, g are six digit;If a = e, b = f and c = = g then which of the given informations is not correct?
(1) If g = 4 then N is divisible by 44.
(2) If a + b + c = 6 then N is divisible by 33.
(3) If g= 8, then for different values of a, b, c and e, N may be a perfect square-Answer
(4) If b = c = 0, then N is not a perfect square.

10. N = abcd is a four digit number and M= xyz is a three-digit number. N M is
(1) a five digit number when a = x= 1
(2) a six digit number when a = 3 and x = 3
(3) a seven digit number when a = 6 and x = 2-Answer
(4) an eight digit number when a = b = c = d = x = y = z = 9

11. N = (A7A)17 is a perfect square. Which of the following statement is FALSE?
(1) A is an even digit.
(2) A is divisible by 3
(3) When N is divided by 13 we get remainder 3. -Answer
(4) None of these

Directions Q. 12 - 13: Read the following information carefully and answer the questions given below.

The above diagram shows the liking of Tea and coffee(hot drink) and coke (cold drink) among students in a particular class. This diagram is based on the survey conducted in the month of February.

12. When another survey was conducted in June among the same students the result was different. All of them liked Coke. 12 liked Tea, but no one liked Coffee. How many students liked only Coke?
(1) 40
(3) 20
(4) 11

13. When another survey was conducted in December among the same students, the result was again different. All of them liked at least one hot drink. 16 liked Coke. No one liked all the three drinks. Which of the following conclusions is true?
(1) No one liked Coke and Coffee.
(2) Some liked Coke and Tea.
(3) Number of students who liked both Tea and Coffee is less than 20. -Answer
(4) Only 10 liked both Tea and Coffee

14. A mother purchase three shirts of the same color but of different size for her three sons.
All the three shirts were kept in a box in a dark room. The three boys took one shirt each at random from the box. What is the probability that none of the boys this own shirt?
(1) ½
(3) 2/3
(4) 1/4

15. Product of three consecutive numbers is 2730. What is the sum of three numbers?
(1) 39
(3) 45
(4) None of these

Directions Q. 16 – 18: Read the following information carefully and answer the questions given below.

The above figure shows the roadmap plan of 5 towns A, B, C, D and E. The computerised car has the software of this roadmap plan in its computer. To follow the route the driver has to feed instructions. Not necessarily all of the instructions at one time, into the computer. One instruction can be used for more than one time in a single set of instructions. The three types of instructions are as follows:

Instructions Type Explanations of instructions
GOTO (X, Y) The car is instructed to move from x to y through shortest route.
ROUTE (X, Y, Z) The car is instructed to move from X to Z via the town Y; Y is situated on the shortest route from X to Z.
BACK (X, Y) The car is instructed to go from X to Y and back to X through shortest route.

16. A person lives in town A. He has to reach E. He wants to visit all the other three towns.What set of instructions should he feed into the computer so that he travels the minimum distance?
(1) GOTO (A, D), GOTO (D, B), GOTO (B, A) ROUTE (A, C, E)
(2) BACK (A, C), ROUTE (A, D, B), GOTO (B, E)
(3) BACK (A, C), GOTO (A, D), GOTO (D, B) GOTO (B, E)-Answer
(4) None of these

17. Mr. Goswami lives in town B. He has to go to town C. he wants to visit all the other three towns. He plans his routes such that he can travel for minimum distance. Find the minimum of instructions to be fed into the computer.
(2) 4
(3) 5
(4) None of these

18. The direct road from A to D is destroyed to flood. A person wants to use the computerised car to go from A to D. which of the th ree set of instructions can’t be used by him?
(1) ROUTE (A, B, E) , GOTO( (E, D)
(2) GOTO (A, B), GOTO (B, D)
(3) ROUTE (A, C, E) , GOTO ( E, D) -Answer
(4) None of these

19. A circle is instructed in a regular octagon. The same circle circumscribes a regular hexagon. Find the ratio of the areas of the circle, the hexagon and octagon.
(1) 2 : 3 3 : 16( 2 –1) -Answer
(2) : 3 3 : 4( 2 –1)
(3) 2 /3 : 2 3 : 4( 2 –1)
(4) None these.

20. Find the remainder when N = 1821 1823 1827 is divisible by 12. (1) 9 (2) 12 (3) 15 (4) 18

Directions: Q 21 - 25: are based on the following:

Sun Ltd. and Star Ltd. are two rivals always trying to outdo each other. The following table gives the payoffs for Sun Ltd. for various strategies that they adopt and the correspon ding strategies adopted by Star Ltd. e.g. If Sun Ltd. adopts strategy B, and Star Ltd. adopts strategy A, then Sun Ltd. gains 6000 while Star Ltd. loses 6000. In addition to this, for implementing any particular strategy, both have to incur certain expenses, which are given in the table “Expenses

21. If Star Ltd. adopts strategy A, which strategy should Sun Ltd. adopt for maximum gain?
(2) B
(3) C
(4) A or C

22. If Star Ltd. adopts strategy B, what is Sun Ltd.’s maximum possible gain?
(1) 10000
(3) 12000
(4) None of these

23. If Sun Ltd. adopts strategy B, what strategy should Star Ltd. adopt to minimise Sun’s gain, regardless of what its own gain will be?
(1) A
(3) C
(4) A or C

24. Of the following, which would be the most intelligent move on the part of Star Lt d?
(1) If Sun Ltd. adopts strategy A, adopt strategy B.
(2) If Sun Ltd. adopts strategy B adopt strategy B. -Answer
(3) If Sun Ltd. adopts strategy C adopt strategy B.
(4) If Sun Ltd. adopts strategy C adopt strategy A.

25. If both the companies adopt strategy C, then which of the following is true?
I. Star Ltd.’s net loss is 12000. II. Sun Ltd.’s gain is 4000.
III. Sun Ltd.’s loss is 4000
(1) I only
(2) I & III -Answer
(3) II only
(4) III only