CAT Question Bank (Quant) - Gaurav Sharma - Set 2
Q38) How many 3-digit numbers have at least 1 even digit?
Q39) x, y, z are positive reals such that xyz = 1, x + 1/z = 5, y + 1/x = 29. Find z + 1/y.
Q40) A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
Q41) A circle is inscribed in an isosceles trapezoid with bases 8 and 18. What is the area of the circle?
Q42) Trapezoid ABCD is inscribed in a circle. Parallel sides AB and CD are 7 inches apart and 6 and 8 inches long, respectively. What is the radius of the circle in inches?
c) 4 root2
d) 5 root2
Q43) A train starts from Delhi at a : b o’clock (i.e. ‘b’ minutes after a o’clock). It reaches Chandigarh on the same day at b : c o’clock after taking exactly ‘c’ hours and ‘a’ minutes. How many different values of a are possible? All the times are given in 24-hour clock format.
Q44) What is the smallest value of x for which x! is divisible by 3^7?
Q45) A triangle is called a p-triangle if the length of each of its side (in units) and its area (in sq. units) are integers. How many of the triangles with the sides (in units) given below are p-triangles?
(i) 4, 5 and 6
(ii) 3, 4 and 5
(iii) 5, 8 and 9
(iv) 5, 6 and 8
(a) One (b) Two (c) Three (d) Four
Q46) Two friends – Prakash and Arpit – started running simultaneously from a point P in the same direction along a straight running track. The ratio of the speeds of Prakash and Arpit was 2 : 5 respectively. Two hours later, Arpit turned back and started running backwards at one-fifth of his original speed. He met Prakash at a distance of 10 km from the point P. What was Prakash’s running speed?
Q47) A tank has four inlet pipes such that each inlet pipe while working independently can fill the tank in 4 hours. The tank also has two outlet pipes such that each outlet pipe while working independently can empty the tank in 3 hours. If all the six pipes are opened simultaneously, then in how much time will the tank get filled completely?
(a) 2.0 hours
(b) 3.0 hours
(c) 2.5 hours
(d) 7.0 hours
Q48) A cubical container is half filled with water. The container is now inclined in such a way that the water surface touches one edge completely and does not touch the other lateral face of the cube which it was touching before inclination.What is the angle made by the surface of water with the bottom surface of the container?
Q49) The average market price of three shares A, B and C is Rs. x. Shares A and C lose Rs. y each and B gains Rs.y/2. As a result, the average market price of the three shares decreases by Re. 1. The value of y is
(d) dependent on x
Q50) Let f(x) = ax^2 + bx + c, where a, b and c are real numbers and a ≠ 0. If f(x) attains its maximum value at x = 2, then what is the sum of the roots of f(x) = 0?
Q51) x/y = 19.636363...... and x and y are coprime, then find x + y
Q52) If LCM of numbers from 1 to 20 is N then find the LCM of numbers from 1 to 35
Q53) 'ab' is a two-digit prime number such that one of its digits is 3. If the absolute difference between the digits of the number is not a factor of 2, then how many values can 'ab' assume?
Q54) A and B start running simultaneously on a circular track from point O in the same direction. If the ratio of their speeds is 6 : 1 respectively, then how many times is A ahead of B by a quarter of the length of the track before they meet at O for the first time?
Q55) There are 3 solutions
Solution 1: Consists of A and B in the volume ratio 3 : 2.
Solution 2: Consists of B and C in the volume ratio 1 : 4.
Solution 3: Consists of B and C in the volume ratio 7 : 3.
The 3 solutions are mixed in the volume ratio X : 3 : 2. If the percentage composition of A and B are equal in the resultant mixture, then what is the value of X?
Q56) How many five-digit numbers can be formed so that at even place there is an even digit and at odd place there is an odd digit, repetition of digits is not allowed? (Assume zero is an even number)
Q57) 2^29 is a nine digit number with each distinct digit. Which digit is not used?