CAT Question Bank (Quant)  Gaurav Sharma  Set 1

Q58) Natural number 'a' is the smallest of 50 consecutive natural numbers. If the sum of these 50 numbers is a perfect square, how many different values of 'a' are possible?
a) Zero
b) One
c) Two
d) More than two

Q59) In a class of 60 students, the average age of the 25 girls is 12 years and that of the boys is 18 years.Three of the students aged 18, 19 and 20 years leave the class and are replaced by 4 students of ages 10, 11, 10 and 11 years. Find the change in the average age of the class .
a) 0.167 years
b) 0.25 years
c) 1.2 years
d) 0.5 years

Q60) In how many ways can 18 identical white balls and 16 identical black balls be arranged in a row so that no two black balls be together ?

Q61) What would be last two digits of (451^41)  (41^451) ?

Q62) 5 points selected on circumference of circle. Find probability that they lie in same semicircle.

Q63) From a point in the interior of an equilateral triangle, the perpendicular distances of the sides are, √3 cm, 2√3 cm and 5√3 cm. The perimeter (in cm) of the triangle is
a. 48
b. 51
c. 57
d. 63

Q64) The product of digit is a Factor of a two digit number. Number of such digit are:
a. 3
b. 5
c. 9
d. 27

Q65) Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle thus formed with the original triangle is,
a. 3:1
b. 2:1
c. 3:2
d. None

Q66) What will be the effect on its area of a triangle if it’s height is decreased by 40% and it’s base is increased by 40%?
a) No change
b) 8% decrease
c) 16% decrease
d) 16%increase

Q67) A regular hexagon is formed by cutting the corners of sides of an equilateral triangle of side 6 cm.The area of this hexagon will be

Q68) The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq cm) of the triangle is
a. 72
b. 83
c. 94
d. None

Q69) There is a tunnel connecting city A and B. There is a CAT which is standing at 3/8 the length of the tunnel from A. It listens a whistle of the train and starts running towards the entrance where, the train and the CAT meet. In another case, the CAT started running towards the exit and the train again met the CAT at the exit. What is the ratio of their speeds?

Q70) Ajay can swim a certain course against the river flow in 84 minutes; he can swim the same course with the river flow in 9 minutes less than he can swim in still water. How long would he take to swim the course with the river flow?

Q71) A policeman starts chasing a thief. The ratio of the speeds of the thief and the policeman is 9 : 11 and when the policeman catches the thief it is found that the policeman has covered 60 meters more than the thief. How much distance did the police have to run to nab the thief?

Q72) Two trains start simultaneously, one from Bombay to Kolkata and other from Kolkata to Bombay. They meet each other at Nagpur which is at a distance of 700 kms from Bombay. If the distance between Bombay and Kolkata is 1600 km, find the ratio of their speeds.

Q73) A thief escapes from a prison at 2 pm and travels away at a speed of 30 kmph. The police realize the escape at 3:30 pm and start the chase then at a speed of 40 kmph. At what time will the police catch the thief? At what distance from the prison is the thief caught?

Q74) Mr. Chaalu while buying clothes uses a faulty meter tape which actually measures 110 cm for a meter and while selling them he uses another faulty meter tape which actually measures 90 cm for a meter. If he buys the cloth at a discount of 5% on the marked price and sells it at a discount of 10% on the same marked price, then what is his percentage gain or loss?
a) 15.8% profit
b) 4.21% loss
c) 5% loss
d) 25% profit
e) None of these

Q75) Sum of all positive integral values of n such that 1002 + n^2 is a perfect square

Q76) How many 5 digit multiples of 3 or 4 (but not both) can be formed using the first 6 natural numbers, if the repetition of digits is not allowed?
a) 432
b) 372
c) 312
d) 240
e) 268

Q77) The number of zeroes in binary notation of 2^389 – 2^350 is