Problem 5 · 2015 Math Kangaroo
Easy
Number Theory
divisibility
Which of the following fractions is not a whole number?
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Answer: D — 20144
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Hint 1 of 2
A fraction is a whole number exactly when the bottom divides the top.
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Hint 2 of 2
Check each numerator for divisibility by its denominator; the one that fails is the answer.
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Approach: test divisibility of numerator by denominator
- 2011/1 = 2011 and 2013/3 = 671 are whole numbers, and 2015/5 = 403 is too.
- But 2014 = 4*503 + 2 is not a multiple of 4.
- So 2014/4 is not a whole number.
- The answer is 2014/4 (D).
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