CAT Question Bank (Quant)  Gaurav Sharma  Set 1

Q19) Ashok travels same distance at 2 kmph on the first day, 4 kmph on second day, 8 kmph on third day and so on. Find Ashok’s average at the end of the 5th day.
a) 5 kmph
b) 5.16 kmph
c) 5.32 kmph
d) 5.64 kmph
e) 6.28 kmph

Q20) For the ninedigit number 2982a7645,following operation is performed:
2 – 9 + 9 – 8  + …+ 6 – 4 + 4 – 5.
For which of the following values of ‘a’ will the above summation be maximum? (  represents the modulus function)
A. 0
B. 2
C. 8
D. 9
E. Both (A) and (D

Q21) Ram said to Rahim, “The unit’s digit of the product of my age and your age is one or the other of three values 2, 4 and 8”. If the age (in years) of Ram and Rahim is R1 and R2 respectively, then find the total number of possible pairs (R1, R2).(Given that R1 and R2 are natural numbers less than 20.)
A. 108
B. 184
C. 128
D. 96
E. 144

Q22) Total number of integer pairs satisfying x + y = xy is ?

Q23) A cube of white chalk is painted red, and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids is not painted red?
(A) 20%
(B) 16 2/3 %
(C) 15%
(D) 25%

Q24) when a number "N" is divided by a proper divisor "d" then it leaves a remainder of 14 and if thrice of that number ie "3N",is divided by same divisor d,the reaminder comes out to be 8.again if 4 times of the same number ie "4N", is divided by d remainder will be?

Q25) The ratio of two six digit numbers abcabc and ababab is 55 : 54. Find the value of a + b + c

Q26) Today is Friday. What day will it be after 4^2010 days?

Q27) What is the remainder when 7^7^7^7^7^7^7.......infinity is divided by 13?
a. 5
b. 6
c. 7
d. None of These

Q28) In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?
A. 56
B. 73
C. 80
D. 120
E. None of the above

Q29) Let an = 1111111.....1, where 1 occurs n number of times. Then,
i. a741 is not a prime.
ii a534 is not a prime.
iii a123 is not a prime.
iv a77 is not a prime.
A. (i) is correct.
B. (i) and (ii) are correct.
C. (ii) and (iii) are correct.
D. All of them are correct.
E. None of them is correct.

Q30) A 25 ft long ladder is placed against the wall with its base 7 ft the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:
A. (2, 7)
B. (5, 8 )
C. (9, 10)
D. (3, 7 )
E. None of the above

Q31) Three runners, A, B and C, are running in the clockwise direction around a circular track. The track is marked with numbers from 1 to 12, uniformly spaced along the track, in the clockwise direction, like the dial of a clock. A overtakes B once at 5 and then the next time again at 9. A also overtakes C once at 2 and then the next time again at 4. If the speed of neither B nor C is greater than half that of A, what is the ratio of B’s speed to C’s speed?

Q32) What is the 625th term of the series where each term is made up of even digits only?
2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, ...

Q33) In a polygon, internal angles have the measures of 90° and 270° only. If there are 18 angles of measure 270°, then what is the number of angles with measure of 90°?

Q34) The sum of all interior angles of eight polygons is 3240°. What is the total number of sides of polygons?

(n1 2)180° + (n2  2)180° + … + (n8  2)180°
= (n1 + n2 + … + n8)180°  16 * 180°
= 3240°
=18 * 180°.
So total number of sides of all polygons is 18 + 16 = 34.

Q35) The houses in a street are spaced so that each house of one lane is directly opposite to a house of other lane. The houses are numbered 1, 2, 3, … and so on up one side, continuing the order back down the other side. Number 39 is opposite to 66. How many houses are there?

Q36) How many positive integers N are there such that 3 × N is a three digit number and 4 × N is a four digit number?

Q37) How many 9digit numbers (in decimal system) divisible by 11 are there in which every digit occurs except zero?