Anna thinks of an integer. It is not a multiple of three. It is not a perfect square. The sum of its digits is a prime number. What could be the integer that Anna is thinking of?
Solution
12 and 21 are multiples of 3 (12 = 4 \times 3 and 21 = 7 \times 3) so the answer is not (A) or (D). 16 is a perfect square (16 = 4 \times 4) so the answer is not (C). The sum of the digits of 26 is 8, which is not a prime number, so the answer is not (E). Since 14 is not a multiple of a three, 14 is not a perfect square, and the sum of the digits of 14 is 1 + 4 = 5 which is prime, then the answer is 14, which is choice (B).
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