Abigail is thinking of a positive integer m. She supplies the following four clues regarding her number.
(a) If m > 20 then m is divisible by 7
(b) If m < 40 then m is 1 less than a multiple of 3
(c) If m > 60 then m is prime
(d) If m < 80 then m is a perfect square
What is Abigail's number?
We can solve this by finding which range 'm' falls in.
If m is in range 0 < m < 20, clues b and d apply. But this is not possible as no perfect square below 20 is 1 less than a multiple of 3, so m cannot be in range 0 < m < 20
If m is in range 20 < m < 40, clues a, b, and d apply. This is not possible as for m to be a multiple of 7 and be a perfect square, m would have to be m = 49, but that is not less than 40 therefore m cannot be in range 20 < m < 40 either.
Moving on, if m is in range 40 < m < 60, clues a and d apply. As stat5ed earlier, for m to be a perfect square and a multiple of 7, it would need to be 49, and m is in this range and satisfies both clues, therefore m = 49.