# Quant Question Bank by VP - Set 2

• Q60) The coefficients of how many terms in the expansion of (x + y – z)^100 are negative?

• Q61) K = (p + q + r)^15. Find the number of distinct terms in the expansion of the bracket.
(1) 136
(2) 153
(3) 145
(4) 120
(5) 128

• Q62) How many five-digit numbers divisible by ‘9’ can be formed using the digits 0, 1, 2, 4, 6, 8, 9 such that each digit occurs atmost once in any such number?

• Q63) In a society, the newspapers of only three languages – Marathi, Gujarati and Hindi – are distributed. Each family residing in the society reads newspapers of at least one of the three languages. The total number of families reading newspapers of exactly one language can be divided into three types only Marathi, only Gujarati and only Hindi. These three numbers are in A.P., in no particular order. Similarly, the three types of families reading newspapers of exactly two languages are also in A.P. The number of families reading newspapers of all the three languages is one-tenth of the number of families reading only Gujarati newspapers, which in turn is two-third of the number of families reading only Hindi newspapers. The number of families reading both Marathi and Gujarati newspapers is 15, whereas the number of families reading both Gujarati and Hindi newspapers is 19. The number of families reading Hindi newspapers is 70, which is more than the number of families reading Marathi newspapers.

What is the total number of families in the society?
(a) 111
(b) 113
(c) 128
(d) Cannot be determined

What is the number of families reading both Marathi and Hindi newspapers?
(a) 11
(b) 21
(c) 23
(d) Cannot be determined

• Q64) Given below is the sequence of all the natural numbers which don’t contain the digit ‘0’.
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13…
What is the 200th term of this sequence?

• Q65) How many negative integer solutions exist for x^2 – y^2 = 400?

• Q66) X is the set of all pairs (q, p) where p and q satisfy N ≥ p > q ≥ 1, where N ≥ 4. If any two distinct members in X have one number in common, they are called “mates”. Otherwise they are called “non-mates”. For example if N = 4, then X = {(3, 4), (2, 3), (2, 4), (1, 2), (1, 3), (1, 4)}. In X, (1, 3) and (1, 4) are mates (2, 3) and (3, 4) are also mates but (3, 4) and (1, 2) are non-mates.

For any N, the number of non-mates of each
member of X is
(1)1/2(N^2 − 3N + 2)
(2) 2N − 5
(3) 3N − 10
(4)1/2(N^2 − 5N + 6)
(5)1/2(N^2 − 7N + 16)

For any N, the number of common mates of
two mates in X is
(1) N − 2
(2) 3N − 8
(3)1/2(N^2 − 6N + 12)
(4) N − 1
(5)1/2(N^2 − 3N)

• Q67) Siddharth has only three types of toys - Cars, Puzzles and Planes. All his toys except 25 are Planes. All except 32 are Cars. All except 27 are Puzzles. How many Cars does he have?

• Q68) In the Wimbledon Tennis tournament of 2014 players ranked 1 to 64 participated. In the first round, the first match was played between the top ranked i.e. 1st ranked and the lowest ranked i.e. 64th ranked players, the second match was played between 2nd ranked and 63rd ranked players and so on. In the next round, the winner of match 1 played against the winner of match 32, winner of match 2 played against the winner of match 31 and so on. This pattern continued in the subsequent rounds as well, till the final.
Que: If there was no upset in the 1st and 3rd rounds and all matches in second round were upsets, the highest ranked player who could win the final was

• Q69) There is a leak which can empty the completely filled container in 10 hours. If the container is full of milk and a tap is opened that fills 4 liters of milk per minute in the container, then the leak takes 15 hours to empty the container. How many liters of milk does the container hold?

• Q70) Once Anil gave Rs.878787878787 to Mukesh and Rs.787878787878 to Nita without any interest. Mukesh and Nita decided to return the due amount of money with a monthly installment equal to the greatest common divisor of the two sums. How many more months does Mukesh require than Nita to return the money?
a) 3
b) 9
c) 27
d) 1

• Q71) Bhavya takes 9 days and Siddharth takes D days to complete a job working alone. Bhavya and Siddharth workon the job on alternate days. If they take exactly the same time irrespective of who starts the job,how many positive integer values are possible for D?
(a) 1
(b) 2
(c) 3
(d) 4

• Q72) How many integer solutions exist for x^2 - 3y^2 = 1376

• Q73) A, B, C are three points such that AB = BC = AC. A circle is drawn passing through A, B, and C. P is a point on the arc joining B and C. Which of the following is true?
a) PA = 2PB + PC
b) PA = PB + 2PC
c) PA = PB + PC
d) PA < PB + PC

• Q74) How many positive integer solutions are possible for the equation 4a + 5b + 2c = 111

• Q75) By selling a sofa set at 85% of the labelled price, Apex furniture earned a profit of 13.33% when it sold the sofa set for Rs. 17,000. What will be the profit percentage if the discount is not offered?

• Q76) The sum of 20 natural numbers is 300. One of the numbers is 1, and another is 100. The largest among the remaining 18 numbers must be at least

• Q77) A bouquet of 25 flowers is to be made out of 4 different types of flowers, namely Rose, Sunflower, Jasmine and Carnation. Sufficientnumbers of flowers are available of each type. Minimum five roses and five sunflowers must be used. At least one flower of each othertype must be used while making the bouquet. Calculate the total number of ways in which the flowers for the bouquet can be selected.

• Q78) The sum of the squares of three consecutive integers is a perfect square. How many such triplets exist?

• Q79) Find the number of 3-digit numbers that can be formed using the digits 1, 2, 3, 4 and 5, without repetition of digits, such that they are divisible by 6

71

199

43

145

164

102

151

45