Question

if a number is divided by 3 and 5, the remainder is 1. if it is divided by 7, there is no remainder. What number between 1 and 100 satifies these conditions.

Answer 1

From these clues:

The number is 1 more than a multiple of 15.

The number is a multiple of 7.

Checking the numbers that are 1 more than a number of 15:

16, 31, 46, 61, 76, 91

91 = 7 × 13

The number is 91.