# CAT Question Paper – Quantitative Ability Questions

**CAT Sample Question Paper**

**CAT Sample Questions – Quantitative Ability Questions**

**D****I****R****E****C****TIONS for questions 1 to 6: Answer the questions independently of each other.**

**1****. The total cost of 2 pencils, 5 erasers and 7 sharpeners is Rs.30, while 3 pencils and 5 sharpeners cost Rs.15 more than 6 erasers. By what amount (in Rs.) does the cost of 39 erasers and 1 sharpener exceed the cost of 6 pencils?**

(1) 20

(2) 30

(3) It does not exceed

(4) Cannot be determined

**2****. If the roots of the equation ( x + 1) (x + 9) + 8 = 0 are a and b, then the roots of the equation (x + a) (x + b) – 8 = 0 are**

(1) 1 and 9

(2) -4 and -6

(3) 4 and 6

(4) Cannot be determined

**3****. What is the remainder when 7****70****0 ****i****s divided by 100?**

(1) 1

(2) 61

(3) 41

(4) 21

**4****. Balram, the local shoe shop owner, sells four types of footwear – Slippers (S), Canvas Shoes (C), Leather Shoes (L) and Joggers (J). The following information is known regarding the cost prices and selling prices of these four types of footwear:**

**(****i****) L sells for Rs.500 less than J, which costs Rs.300 more than S, which, in turn, sells for Rs.200 more than L.**

**(****ii****) L costs Rs.300 less than C, which sells for Rs.100 more than S,**

**w****hich, in turn, costs Rs.100 less than C.**

**I****f it is known that Balram never sells any item at a loss, then which of the following is true regarding the profit percentages earned by Balram on the items L, S, C and J represented by l, s, c and j respectively?**

(1) *l *≥ *c *≥ *s *≥ *j *(2) *c *≥ *s *≥ *l *≥ *j *(3) *l *≥ *s *≥ *c *≥ *j *(4) *s *≥ *l *≥ *j *≥ *c*

**5****. A sequence of 4 digits, when considered as a number in base 10 is four times the number it represents in base 6. What is the sum of the digits of the sequence?**

(1) 7 (2) 6 (3) 9 (4) 8

**6. ****Some friends planned to contribute equally to jointly buy a CD player. However, two of them decided to withdraw at the last minute. As a result, each of the others had to shell out one rupee more than what they had planned for. If the price (in Rs.) of the CD player is an integer between 1000 and 1100, find the number of friends who actually contributed?**

(1) 21 (2) 23 (3) 44 (4) 46

**D****I****R****E****C****TIONS for questions 7 and 8: Answer the questions on the basis of the information given below.**

**A robot is designed to move in a peculiar way and it can be set in motion by a microprocessor program. The program can be initiated by assigning a positive rational value to its variable n. The program directs the robot to move in the following way. As soon as the program is started, the robot starts from the point O, moves 2n metres northward and changes its direction by n° to the right. It then moves 2n metres forward and again changes its direction by n° to the right and continues in this manner till it reaches the starting **

**point O, or till it covers a total distance of 1000 m, whichever happens first, and then it stops.**

**7. I assigned a value for n and started the program. If the robot finally came back to O and stopped, what is the total distance that it has covered?**

(1) 180 m (2) 360 m (3) 720 m (4) Cannot be determined

**8. For how many values of n in the intervals [1, 60] does the robot cover less than 1000 m, before it stops?**

(1) 19 (2) 60 (3) 355 (4) Infinite

**D****I****R****E****C****TIONS for questions 9 to 17: Answer the questions independently of each other.**

**9. If N = 888Dup to 100 digits, what is the remainder when N is divided by 625?**

(1) 128 (2) 138 (3) 338 (4) 388

**10****. If [log****10****1****] + [log****10****2****] + [log****10****3****] + [log****10****4****] + …… + [log****10***n***] = n, where [x] denotes the greatest integer less than or equal to x, then**

(1) 96 ≤ *n *< 104 (2) 104 ≤ *n *< 107 (3) 107 ≤ *n *< 111 (4) 111 ≤ *n *< 116

**11****. A regular polygon has an even number of sides. If the product of the length of its side and the distance between two opposite s****i****des is of its area, find the number of sides it has.**

(1) 6 (2) 8 (3) 20 (4) 16

**12****. There are three cities A, B and C, not on the same straight road. Two buses P and Q start simultaneously from A and B respectively towards C. By the time Q reaches C, P is exactly halfway to C. Immediately after Q reaches C, it starts travelling towards A and it ****c****rosses P at a point 165 km from A. The ratio of the speeds of P and Q is 3 : 5. Assume that the roads joining A to C, B to C and B to A are all straight roads. If B is twice as far as from A as it is from C a****nd P would take to cover the distance from A to B, how much time would Q take to cover the distance from C to A?**

(1) 2 2/5 hours (2) 3 hours (3) 3 3/5 hours (4) 4 hours

**13****. Two positive real numbers, a and b, are expressed as the sum of m positive real numbers and n positive real numbers respectively as follows:**

*a ***= s**

**1**

**+**

*s***2**

**+ D..+**

*s*

*m***a**

**nd**

*b ***= t**

**1**

**+**

*t***2**

**+ D..+**

*t*

*n***I****f [ a] = [s**

**1**

**] + [**

*s***2**

**] + D.. + [**

*s*

*m***] + 4 and [**

*b*] = [*t***1**

**] + [**

*t***2**

**] + D. + [**

*t*

*n***] + 3,**

**w****h****e****re [ x] denotes the greatest integer less than or equal to x, what **

**i**

**s the minimum possible value of**

*m*+*n*?(1) 6 (2) 10 (3) 8 (4) 9

**14****. Consider two figures A and D that are defined in the co-ordinate plane. Each figure represents the graph of a certain function, as defined below :**

**A****: | x | – | y | = a**

**D****: | y | = d**

**I****f the area enclosed by A and D is 0, which of the following is a possible value of ( a, d)?**

(1) (2, 1) (2) (-2, 1) (3) (-2, 3) (4) (2, 3)

**15****. A natural number n is such that 120 n ≤ 240. If HCF of n and 240 is 1, how many values of n are possible?**

(1) 24 (2) 32 (3) 36 (4) 40

**16****. If the sum to infinity of the series 2 + (2 – d)2/3 + (2 + d) 4/9 + (2**

**+ 3**

*d*) 8/27 + D.. is 5/2, what is the value of*d*?(1) 7/12 (2) -7/12 (3) -5/12 (4) 5/12

**17****. The first n natural numbers, 1 to n, have to be arranged in a row from left to right. The n numbers are arranged such that there are an odd number of numbers between any two even numbers as well as between any two odd numbers. If the number of ways in which this can be done is 72, then find the value of n.**

(1) 6 (2) 7 (3) 8 (4) More than 8

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