math ( sets )

{ 30,31,32,....,100 }

How many numbers in the above set are divisible by 8 ?

a. 9
b. 10
c. 11
d. 12
e. 13

please answer and explain

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asked by Thomas
  1. Multiples of 8:

    32, 40, 48, 56, 64, 72, 80, 88, 96

  2. only 1 in 8 will be divisible, so divide by 8.

    (100-30+1)/8 = 8.8
    so, there appear to be only 8 multiples of 8 in that set.

    But, the non-multiples on either end take up some of the candidate spots. So, start just after the smallest multiple of 8:

    (100-31)/8 = 8.6

    So, there are 8 multiples of 8 between 33 and 100, as well. Add in 32, and we have 9 altogether:

    32 40 48 56 64 72 80 88 96

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    posted by Steve

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