The total number of two-digit positive integer lesser than 100, which are not divisible by 2, 3 and 5 is ?



The total number of two-digit positive integer lesser than 100, which are not divisible by 2, 3 and 5 is ?

A. 23

B. 24

C. 25

D. 26

Answer : B. 24


Explanation:

    Numbers less than 100 divisible by 2 are 10, 12, 14, 16,...,98.
    Total numbers divisible by 2 are 45
    Remaining numbers are 11, 13, 15, 17, 19...99 = 45

    Numbers divisible by 3 in the above numbers are 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93 and 99.
    Total numbers divisible by 3 are = 15
    Remaining integers = 45-15 = 30.

    Numbers divisible by 5 in the remaining numbers = 25, 35, 55, 65, 85, 95
    Total numbers = 6
    Remaining 30-6 = 24.

    So 24 numbers are not divisible by 2, 3 and 5.



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