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A baker packs muffins into gift boxes, and each box holds exactly 6 muffins with none left over. Which of the following could be the total number of muffins the baker packs?
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Correct answer
E
Packing into boxes of 6 with none left over means the total is a multiple of 6, so it needs a factor of 2 and a factor of 3. Factor each candidate instead of eyeballing: 48 = 6 × 8 passes both tests, choice (E).
The slate is built to punish half-checking. (B) 44 = 2 × 2 × 11 and (D) 46 = 2 × 23 are even but carry no 3. (C) 45 = 3 × 3 × 5 has the 3 but is odd. (A) 40 ends in a friendly zero, yet 40 = 2 × 2 × 2 × 5 has no 3 either.
An even number, or a round one, is not automatically a multiple of 6; demand both prime factors before you accept it: 48.
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