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

Answer 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.