# CAT Question Bank (Quant) - Gaurav Sharma - Set 2

• Q92) A train met with an accident 150 kms from station A. It completed the remaining journey at 5/6 of previous speed and reached 15 mins late at station B. Had the accident taken place 30 km further, it would have been only 7 mins late. Find the speed of the train and distance between A and B.

• Q93) On a circle there are 10 points each of which is connected with each other with a straight line. How many triangles will be formed which lies completely inside the circle?

• Q94) In Cricket, a batsman can score 0, 1, 2, 3, 4 or 6 runs of a ball. What is the number of distinct sequences in which exactly 30 runs can be scored in an over of six balls? Assume that all the runs are scored by batsmen only and there are no extra balls/runs.
(a) 36
(b) 71
(c) 77
(d) 86

• Q95) In how many ways can 83 be expressed as the sum of two natural numbers that are coprime to each other?

• Q96) Find all prime numbers p for which 5p + 1 is a perfect square

• Q97) If in a certain number system the difference of 5333 and 555 is 4445 then find the sum of the numbers 5333 and 555

• Q98) When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
a) 11
b) 17
c) 13
d) 23
e) None of these

• Q99) A two-digit natural number is ‘q’ times the sum of its digits. The number formed by interchanging the digits is how many times the sum of its digits?
a) 9 - q
b) q + 1
c) q - 1
d) 11 - q

• Q100) There are 2n consecutive natural numbers. If (n + 1) numbers are randomly selected, then what is the probability that their HCF is 1?

• @gaurav_sharma Ans (a)2
average market price of 3 shares decreased=3*1=3
if y=2
then
a +c -b=3
y+y-y/2=3
2+2-1=3

138

127

136

92

145

107

106

169