Maths Olympiad Prep

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Problem 200

Algebra Difficulty 1.7 Find the answer CEMC Pascal

Which of the following divisions is not equal to a whole number: 6012\frac{60}{12}, 608\frac{60}{8}, 605\frac{60}{5}, 604\frac{60}{4}, 603\frac{60}{3}?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Since 608=60÷8=7.5\frac{60}{8}=60 \div 8=7.5, then this choice is not equal to a whole number. Note as well that 6012=5,605=12,604=15\frac{60}{12}=5, \frac{60}{5}=12, \frac{60}{4}=15, and 603=20\frac{60}{3}=20 are all whole numbers.

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