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ACT Sample Questions : Mathematics

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

    Answer: 2

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

    Ans :C

63. 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

64. 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

65. 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

66. '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

67. 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

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

    Ans :C

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

    Ans :C

70. 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