Quant Question Bank by VP  Set 2

Q40) If the highest power of 20 in n! is x, then x can take the following values except
a. 27
b. 28
c. 30
d. 31

Q41) Three horses : Kanishka, Silver Streak and Arabian Knight are the only horses competing in a race and
only one of these three can win the race. If Kanishka is twice as likely to win as Silver Streak and SliverStreak is twice as likely to win as Arabian Knight, then what is the probability of Arabian Knight losing this race?

Q42) In how many ways can 3 identical books be distributed among 5 students such that no student gets more than 2 books?

Q43) There is a railway line that passes through a tunnel of length 200 metres. A road runs parallel with the
tunnel. One day when the driver of a 150 metre long train is exactly at the middle of the tunnel, a man Schumi, who is on the road parallel to the tunnel starts from one of the ends of the tunnel towards the other end. If Schumi and the train cross the tunnel simultaneously, then what is the ratio of the time taken by them to cross each other when they move in the same direction to the time taken by them to cross each other when they move in the opposite direction

Q44) On any given day, the bank balance of a person A is the sum of his bank balance on the previous day
and his bank balance on the next day. If the bank balance of A on 18th November 2007 and 19th November 2007 is Rs.4000 and Rs.2000 respectively, then what will be his bank balance on 16th November 2008? (Assume that the bank balance of A can be negative.)

Q45) Nando starts reading all the letters of the English alphabets starting from ‘a’ at the rate of 1 letter per second. Nachi, his younger brother reads the vowels only starting from ‘a’ at the rate of 1 vowel per second. This cycle of reading letters at the uniform rate continues indefinitely. If the two of them start reading together, after how much time, will they just complete reading the letter ‘u’ together?

Q46) There is a group of 11 people namely: A1, A2, A3 ... A11. The number of balls with A1 through A11 in that order is in arithmetic progression. If the number of balls with A1, A3, A5, A7, A9 and A11 is equal to 72, then what is the number of balls with A1, A6 and A11 put together?
(a) 24
(b) 36
(c) 48
(d) Cannot be determined

Q47) g(P) represents the product of all the digits of P, e.g. g(45) = 4 × 5.
What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?

Q48) In a triangle ABC, the incircle touches the three sides AB, BC and CA at the points D, E and F respectively. If the length(in cm) of the sides AB, BC and CA are three consecutive even numbers, then which of the following cannot be the radius (in cm) of the incircle?
(a) √3
(b) √7
(c) √15
(d) √32

Q49) Let M be a threedigit number denoted by ‘ABC’ where A, B and C are numerals from 0 to 9. Let N bea number formed by reversing the digits of M. It is known that M – N + (396 × C) is equal to 990. How many possible values of M are there which are greater than 300?

Q50) There are 100 questions in a test paper. Four marks are awarded for each right answer and two marks
are deducted for each wrong answer. If Abhilash attempts more than 85 questions and get 70 marks, What is the minimum number of questions that he could have answered correctly?

Q51) Amar, Bhuvan, Chetan and Dinesh are four friends. Amar has m marbles with him. He gives Bhuvan 1 less than half the number of marbles he has. Then he gives Chetan 1 less than half the remaining number of marbles he has. Finally, Amar gives Dinesh 1 less than half the remaining number of marbles he has and is
left with 4 marbles. Which of the following best describes the value of m?
(1) 1 ≤ m ≤ 4
(2) 5 ≤ m ≤ 9
(3) 9 ≤ m ≤ 13
(4) 10 ≤ m ≤ 14
(5) m ≥ 14

Q52) If 3a + 5b + 7c = 1.25 k and 2a + b + 3c = 0.75 k, then 7b + 5c is what percentage of k?
a) 25%
b) 50%
c) 35%
d) 75%

Q53) There are some two rupee coins and five rupee coins in a bag. If the number of five rupee coins is tripled, then the amount in the bag is increased by 75%. Which of the following can be the number of five rupees coins in the bag?
a) 13
b) 20
c) 18
d) 32

Q54) One of the roots of the equation x^2 + bx + 2b = 0 (where b is a real number) is twice the other root.
Which of the following is the equation whose roots are ‘b’ and ‘b + 1’?
(a) x^2 + 19x – 90 = 0
(b) x^2 –9x + 20 = 0
(c) x^2 + 9x – 90 = 0
(d) x^2 – 19x + 90 = 0

Q55) A = k^2 – 1 and B = (k + 1)^2 – 1, where k is a natural number greater than 1. How many prime numbers are there by which both A and B are divisible for at least one value of k?

Q56) A 1litre wateralcohol mixture M1 contains 40% water while another 1litre wateralcohol mixture M2 contains 70% water. x ml is taken out from each of the two mixtures and put in two separate containers. The quantity taken out from M1 is mixed into the remaining part of M2 and the quantity taken out from M2 is mixed into the remaining part of M1. If the two mixtures contain equal quantities of water after the operation, then what is the value of x?

Q57) The work done by 2 men in a day is equal to the work done by 3 children in a day. The work done by 3 men in a day is equal to the work done by 5 women in a day. It takes 10 days for a man, a womanand a child to complete a job working together. How many days will 2 children working together taketo complete the same job

Q58) How many fivedigit numbers divisible by 4 can be formed using the digits 0, 7, 5, 2, 4, 6 without repeating any digit?

Q59) There are 40 lines in a plane of which a set of 12 lines are concurrent at A, another set of 15 lines are concurrent at B and the set of remaining lines are parallel. What is the number of points of intersection of these 40 lines, given that the three sets are disjoint?