CAT Sample Questions

Quantitative Section : Quantitative Sample Questions

Number System

141. The largest number amongst the following that will perfectly divide 101100 - 1 is
     1. 100
     2. 10000
     3. 100¹⁰⁰
     4. 100000

     Ans : 2

142. What is the highest power of 7 in 5000!? (5000! means factorial 5000)
     1. 4998
     2. 714
     3. 832
     4. 816

     Ans :C

143. What is the total number of different divisors including 1 and the number that can divide the number 6400?
     1. 24
     2. 27
     3. 54
     4. 68

     Ans :B

144. How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?
     1. 4! - 3!
     2. 4
     3. 8
     4. 6

     Ans :B

145. A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?
     1. 3
     2. 21
     3. 59
     4. 68

     Ans :C

146. 'a' and 'b' are the lengths of the base and height of a right angled triangle whose hypotenuse is 'h'. If the values of 'a' and 'b' are positive integers, which of the following cannot be a value of the square of the hypotenuse?
     1. 13
     2. 23
     3. 37
     4. 41

     Ans :B

147. What is the reminder when 91 + 92 + 93 + ...... + 99 is divided by 6?
     1. 0
     2. 3
     3. 4
     4. None of these

     Ans :B

148. How many times will the digit '0' appear between 1 and 10,000?
     1. 4000
     2. 4003
     3. 2893
     4. 3892

     Ans :C

149. What is the total number of different divisors of the number 7200?
     1. 20
     2. 4
     3. 54
     4. 32

     Ans :C

150. What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?
     1. 144
     2. 72
     3. 108
     4. 216

     Ans :B