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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?

 Jul 6, 2021
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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.

 Jul 6, 2021

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