Question

54.
{140, 141, 142,…, 298, 299, 300}
How many numbers in the set above are
multiples of 7 but not of 14?
F. 10
G. 11
H. 21
J. 22
K. 23

Answers

  1. We have
    140 = 7·20
    and
    300 = 294 + 6 = 7·42 + 6
    This tells us that there are 42 – 20 + 1 = 23 multiples of 7 in the list. Notice that the first and last multiple are both even. The multiples occur in a pattern of {even, odd, even, odd, …, even} so that 12 (number of multiples plus 1, divided by 2) are even and 11 (23 – 12) are odd.
    So there are 11 multiples of 7 not divisible by 14 in the list.

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