How many whole numbers less than 50 are divisible by 5 or 7 but not both?

Answer 1

14.

Assuming dealing with only counting numbers (ie integers greater than 0):

Numbers divisible by 5 or 7 are their multiples.

50 ÷ 5 = 10 → last multiple of 5 less than 50 is 9 x 5

→ 9 numbers less than 50 are divisible by 5

50 ÷ 7 = 71/7 → last multiple of 7 less than 50 is 7 x 7

→ 7 numbers less than 50 are divisible by 7

Numbers divisible by both are those which are multiples of their lowest common multiple = 35

50 ÷ 35 = 115/35 → last multiple of 35 less than 50 is 1 x 35

→ 1 number less than 50 is divisible by both 5 and 7 and needs to be removed from both the above counts.

→ (9 - 1) + (7 - 1) = 14 numbers less than 50 are divisible by 5 or 7 but not both.

If there is no restriction on numbers being greater than 0, there are infinitely many numbers as it includes the infinite number of negative numbers which are all less than 50 and provide an infinite number of numbers divisible by 5 or 7 but not both.