Quant Question Bank by VP  Set 2

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

Q1) How many integers between 1000 and 9999 have exactly one pair of equal digits, such as 4049 or 9902, but not 4449 or 4040?

Q2) Pipes A and B can completely fill a water tank independently in 4 hrs and 5 hrs respectively. A pipe Ccan empty the tank filled completely with water in 3 hrs. Initially the tank is empty and all the pipes areclosed. Pipe A is opened first at time t = 0 hrs and pipe C is opened at the instant when the tank is exactlyhalf filled with water. Pipe B is opened after pipe C and at the instant when the tank is exactly onefourth filled with water. Find the total time taken to fill the tank completely counting from t = 0 hrs.

Q3) Half of a class of 200 students enrolled for exactly one of the three activities swimming, skating and dancing. Total enrollments were 80 in swimming, 75 in skating and 60 in dancing from the class. Number of students who enrolled for skating and swimming only was 10 more than the number of students who enrolled for skating and dancing only.
Find the minimum possible number of students who enrolled for at least one of the three activities.
(a) 142
(b) 143
(c) 144
(d) 141Find the maximum possible number of students who enrolled for exactly 2 activities?
(a) 57
(b) 56
(c) 55
(d) 54

Q4) A set of 7 pens, 9 erasers and 11 sharpeners cost Rs. 79 and 2 pens, 5 erasers and 8 sharpeners cost Rs. 42. Find the total cost of one sharpener, one eraser and one pen.

Q5) Given that w, x, y and z are natural numbers such that 4w = xyz, 4x = wyz and 4z = wxy. Which of thefollowing is a possible value of (w + x + y – z)^2 ?
(a) 25
(b) 9
(c) 36
(d) 1

Q6) The value of A is given by the square of the volume of a sphere drawn by taking the longest diagonal of a cube as the diameter of the sphere. The value of B is taken as the cube of the sum of the areas of all the circles of maximum radius that can be enclosed inside each of the faces of the above cube. Find A/B

Q7) In a school committee comprising 12 members, there are, exactly two students from each of the class from class 7 to class 12. In how many ways can a subcommitiee of four students be formed, such that no two students in the sub committee belong to the same class.

Q8) How many ordered pairs (P, Q) are there such that the unit’s digits of P^P and Q^Q are the same?
P and Q are natural numbers less than 10 and are not necessarily distinct

Q9) lf the length and breadth of a rectangle are increased by 4 units each, then the area of the rectangle increases by 100%. lf the breadth is Decreased by 6 units and the length is increased by 2 units, then the area decreased by 75%. Find the ratio of the length of the diagonal of the rectangle and the length of the rectangle.

Q10) P is a group of four numbers 1, 2, 3 and 1. In every step, 1 is added to any two numbers in group P. In how many such steps is it possible to make all the four numbers in group P equal?

Q11) A triangle has its longest side as 38 cm. lf one of the other two sides is 10 cm and the area of the triangle is 152 sq cm, find the length of the third side.

Q12) A circle of radius 3 units is drawn with centre as (8,7) and another circle is drawn taking the line segment joining (12, 8) and (4, 4) as diameter. Find the number of common tangents that can be drawn to these two circles

Q13) A boat moves at a speed of 12 kmph in stillwater. lt has to travel a distance of 6O km downstream fromP to Q. The moment the boat reached a point R,between P and Q, the speed of the current suddenlydoubled. lf as a result, the boat reached itsdestination half an hour earlier than it normally would have, what is the speed of the stream ?

Q14) A natural number n is such that 120 ≤ n ≤ 240. If HCF of n and 240 is 1, how many values of n are possible?

Q15) The function f(x) is defined such that f(2x) + f(3x) + f(x + 2) + f(3  x) = x. for all real values of x. Find f(0)

Q16) In an exam there are 90 questions. There are three sections, 1,2,3. Each question in section 1 carries 2 marks, each question in section 2 carries 3 marks, and each question in section 3 carries 4 marks. All questions in section 1 together carry at least 40% of the total marks of the exam. If section 3 has atleast 36 questions, section 1 has how many questions?
a. 52 or 53 or 54
b. 50 or 51 or 52
c. 51 or 52 or 53
d. 52 or 53

Q17) Find the distance between the lines, 2x  5y  9 = 0 and 10y = 4x  93

Q18) There are three containers A, B and C filled with 60%, 75% and 80% solution of alcohol in water. The solution in the three containers are taken in a certain ratio and mixed thoroughly to form a 70% solution of alcohol in water. In this mixture, the quantity of solution taken from C is 40% less than the quantity taken from A. By what percent is the quantity taken from B less or more than the quantity taken from A?

Q19) Y = 2, 3, 4, 5 …., 103
Sm = am : a∈Y, m∈N
Find the least element in the set[Y–(S2∪S3∪S4∪….∪S89)]

Q20) Three natural numbers a, b and c are such that a^2 + b^2= c^2. If a = 20, how many ordered pairs (b, c) are possible?