CAT Question Bank (Quant)  Gaurav Sharma  Set 2

Number of questions : 100
Answer Key Available  No
Topic : Quant Mixed Bag
Source  Genius Tutorials CAT preparation forum

Q1) The midpoints of the adjacent sides of a triangle are joined. The midpoints of the adjacent sides of the resultant triangles are also joined.The ratio of the area of the central small triangle to the original triangle is:
a) 1 : 4
b) 1 : 8
c) 1 : 12
d) 1 : 16
e) 1 : 24

Q2) Adjacent sides of a parallelogram are 21 cm and 27 cm. One of its diagonals is 24 cm in length. Find its other diagonal.
a) 25 cm
b) 42 cm
c) 32 cm
d) 22 cm
e) 45 cm

Q3) 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

Q4) Pure milk contains 89% water how much water should be added to from a sample of 22 liter containing 90% water?

Q5) A container has 100 liters (mixture of milk and water) in the ratio of 3:2. When 40 liters of mixture is taken out and replaced with the same amount of water, what is the ratio of milk and water left in the container?

Q6) Samyak’s wrist watch lagged behind by 12 min on Thursday at 6:00 am while it was 16 min ahead on Saturday at 9:00 pm in the same week. At what time did the watch show the correct time?
a. 9 pm on Friday
b. 9 am on Friday
c. 1:30 pm on Friday
d. 12:30 am on Saturday
e. None of the above

Q7) 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

Q8) What is the sum of the first 46 prime numbers?
a) 3266
b) 3087
c) 4226
d) 3936
e) 4227

Q9) If P Q R are three points on a circle, What is the maximum area of the triangle formed by them where radius of circle is 'a' units?

Q10) Find the no of positive divisor of N^2 such that the positive divisor are less than N and do not divide N completely. where N = 2^17 * 3^9 * 5^3.

Q11) The highest power of 2 in 10! + 11! + 12! + 13! + ...+ 1000! is
(a) 8
(b) 9
(c) 10
(d) 11

Q12) Two points are chosen randomly on the circumference of a circle. What is the probability that the distance between the 2 points is at least 'r', the radius of the circle?

Q13) How many 10digit positive integers with distinct digits are multiples of 11111?
a) 1234
b) 2345
c) 3456
d) 4567
e) None of these

Q14) For how many natural numbers less than 10^5 the sum of their digits equal to 10?

Q15) f is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(– 5) = 5, then the value of f(– 25) + f(25) is
a. 5
b. 10
c. 0
d. 25

Q16)

Q17)

Q18) The sum of 2 five digit numbers AMC10 and AMC12 is 123422. What is A + M + C ?
a) 10
b) 11
c) 12
d) 13
e) 14

Q19) A positive integer n has exactly 4 positive divisors that are perfect fifth powers, exactly 6 positive divisors that are perfect cubes, and exactly 12 positive divisors that are perfect squares. Find the least possible number of possible integers that are divisors of n