Question

If set s consists of all positive integers that are multiples of 2 and 7 both,how many numbers in set s are between 140 and 240 inclusive?

Answer 1

Answer:

A positive integer that is a multiple of both 2 and 7 is a multiple of 14. Since 140 is a multiple of 14, start listing there and count the terms in the range: 140, 154, 168, 182, 196, 210, 224, 238.

Alternatively, note that 140 is the 10th multiple of 14, and 240/14 ≈ 17.143 (use the calculator).

Therefore, the 10th through the 17th multiples of 14, inclusive, are in this range. The number of terms is 17 – 10 + 1 = 8 (“add one before you are done” for an inclusive list).