Quant Question Bank by VP  Set 1

Number of Questions  100
Topic  Quant Mixed Bag
Answer Key available?  No
Source  CAT Prep Forums

Q1) Aman and eight of his friends took a test of 100 marks. Each of them got a different integer score and the average of their scores was 86. The score of Aman was 90 and it was more than that of exactly three of his friends. What could have been the maximum possible absolute difference between the scores of two of his friends?
a) 83
b) 73
c) 54
d) 44

Q2) Manjul bought 5 diamond rings – R1, R2, R3, R4 and R5 – to gift to five of his female friends on their weddings. He also bought five boxes – B1, B2, B3, B4 and B5 – to keep the rings, where B1 was for R1; B2 was for R2; and so on. Then he asked his wife Nalini to pack the rings in the boxes accordingly. Nalini, miffed at her husband’s decision to gift diamond rings to his female friends, decided not to follow the instructions. If she chose to put just two of the five rings into the correct boxes, then in how many ways could she have packed the rings?

Q3) x, y and z are real numbers such that x > 6, y < 0 and z > –2.
How many of the following statements are definitely true?
(i) x + y + z > 0
(ii) xy + yz + zx = 0
(iii) x + y^2 + z^4 < 0

Q4) The sum of the roots of the quadratic equation ax^2 + bx + c = 0 is equal to the sum of the squares of their reciprocals. If a, b and c are real numbers, and a ≠ 0, then bc^2, ca^2 and ab^2 are in
a) G.P.
b) A.P.
c) H.P.
d) None of these

Q5) Find the sum of 6 + (6 + 12) + (6 + 12 + 18) + ... + (6 + 12 + 18 + .. + 1200)

Q6) Six men and two boys working together can complete a piece of work in (9/4) days. If the number of days taken by 5 boys to complete the same work is 4 more than that taken by 3 men, then the efficiency of a boy is what percent that of a man?

Q7) Tn is the nth term of a Geometric Progression such that Tn = T(n1) + T(n2) for n > 2. If the first term and the common ratio of the progression are positive real numbers, then find the common ratio.

Q8) Find the product of all the real roots of the quadratic equation x^2  x  12 = 0

Q9) How many positive integer value solution are there for the equation 6x + 9y = 100 ?

Q10) The product of three natural numbers, N1, N2 and N3, is twelve times their H.C.F. How many ordered triplets (N1, N2, N3) are possible?

Q11) Two articles were sold at a profit of 25% each. The ratio of the profits made on the two articles was6 : 7. If the average selling price of the two articles was 3510, what was the absolute difference between the profits earned on the two articles?

Q12) A circle is inscribed in a regular hexagon and the regular hexagon is inscribed in a circle. By what percentage is the area of the bigger circle more than that of the smaller circle?

Q13) Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you're told that each of the labels are wrong. You may reach into one of the boxes and pull out only one marble. Which box should you remove a marble from to determine the contents of all three boxes?

Q14) The cost price of 6 Dairy Milks is equal to the selling price of 10 Kitkats and the cost price of 6 Kitkats is equal to the selling price of 1 Dairy Milk. The net profit percent on the sale of a Dairy Milk and a Kitkat is 50%. Find the profit percentage on the sale of each Kitkat.[Assume all Dairy Milks are identical and the same applies to Kitkats]

Q15) If a, b, c and d are integers and n is a prime number, then which of the following is always a factor of
(a + b – c – d)^n – (a^n + b^n – c^n – d^n) ?
(a) n
(b) a + b – c – d
(c) n – 2
(d) n + 2

Q16) P is a set of positive integers, such that each of its elements is of the form (3m – 2n), where m and n are distinct natural numbers less than 6. Which element of P can be expressed in the form (3m – 2n) for two distinct sets of values of m and n?
a) 1
b) 3
c) 7
d) 10

Q17) ABCD is a quadrilateral, with all its sides equal in length. The diagonals of the quadrilateral intersect at point O. If AO + BO = 20 units, what is the maximum possible area (in square units) of the quadrilateral?

Q18) Rohan and five of his friends contributed equal money and hired a car to Goa. At least one of his friends pulled out of the trip at the last moment and so they decided to divide the expenses between the rest of the people. During the journey the car required some minor repair for which they paid 250 extra. The total travelling expenses, including the repair charges, amounted to 410 per person. If each of the six friends had contributed an integral amount more than 100 initially, then what was their total initial contribution?

Q19) Find the sum of the digits of the number which is cube of 99999…..9999 (2014 digits).