Question Bank (2)  Quant Mixed Bag  Shashank Prabhu, CAT 100 Percentiler

Number of Questions
Topic  Quant Mixed Bag
Answer Key Available ? : Yes
Source : Learningroots forum

Q1) Instead of dividing Rs. 180 among A, B and C in the ratio (1/3) : (1/4) : (1/6) respectively, it was divided in the ratio 3 : 4 : 6 by mistake. Who gained in this transaction?
[OA: C]

Q2) J and K sit in a circular arrangement along with 10 other people. What is the probability that they will sit together?
[OA: 2/11]

Q3) Hiccup was the guest speaker at a seminar on “How to train your dragon” at the Romanian Dragon Sanctuary. He left his office and traveled at a certain speed so that he would reach the Sanctuary on time. After travelling half the distance, he realised that he had left his laptop at his office. He turned back immediately and increased his speed by 50% and reached his office. As compared to his original speed, by what percent should Hiccup increase his speed so that he still reaches the Sanctuary on time?
[OA: 500%]

Q4) How many numbers greater than 13000 can be formed using the digits 5, 0, 8, 1 and 7 such that each digit is used exactly once?
[OA: 90]

Q5) A man works in a building located 7 blocks east and 8 blocks north of his home. He reaches his office and then walks to a supermarket located 2 blocks east and 4 blocks north of his home. If all the streets in the rectangular pattern are available to him for walking and he always takes the shortest route, how many different routes can he take to go from his house to the supermarket via his office?
[OA: 15C7 * 9C4]

Q6) How many three digit numbers are of the form xyz with x < y, z < y and x ≠ 0?
[OA: 240]

Q7) If 9x + 15xy + 35y = 100, for all real x, y > 0, then find the minimum value of 3x + 5y.
[OA: 12]

Hint: 3x(3+5y)+7(3+5y)=121
(3x+7)(3+5y)=121
Apply either equal terms logic or AM>=GM

Q8) The probability that a builder will get a construction contract is 3/4 and the probability that he will not get the electrical contract is 7/9. If the probability of getting at least one contract is 5/6, what is the probability that he will get both?
[OA: 5/36]

P(getting an electrical contract) = 2/9
So, using basic set theory, 5/6 = 3/4 + 2/9  P(both)
P(both) = 5/36

Q9) There are 4 members in a committee. If one of them is replaced by a younger member such that the average age of the committee is as it was 6 years ago. The new member is how many years younger than the member replaced?
[OA: 24]

Q10) Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A and R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?
[OA: 7.5 hours]

Take the capacity of tank A to be 120 units.
Find out work done per hour by P, Q and R and then use the cumulative work to find out the total time.

Q11) A + 2B + 3C + 4D = 36, where A, B, C and D are positive integers. What is the maximum value of A * (B^2) * C * (D^2)?
[OA: 3888]

Take the numbers as a, b, b, 3c, 2d, 2d and apply AM >= GM.
(a + b + b + 3c + 2d + 2d)/6 >= (a * b * b * 3c * 2d * 2d)^1/6
6^6 >= 12 * a * b^2 * c * d^2
a * b^2 * c * d^2 =< 3888

Q12) A box contains 11 cards. Each card has a number from 1 to 11 (both inclusive) and each number is used exactly once. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?
[OA: 2/33]

For the median to be 3, there have to be 2 numbers less than 3 and two greater than 3. 1 and 2 are automatic choices and so, the other two numbers can be selected from the remaining 8 in 8c2 = 28 ways. Total ways is 11c5 = 462. Probability will be 14/231 or 2/33.

Q13) Number of integer solution of the equation a^12 + 12 = b^4
[OA: 4]

(2,2), (2,2), (2,2) and (2,2)