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, 2020

Number theory Difficulty 1.4 Junior Find the answer Canada

The ratio of apples to bananas in a box is $3\!:\!2$ . The total number of apples and bananas in the box cannot be equal to

$40$
$175$
$55$
$160$
$72$

Your answer

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

Solution

Since the ratio of apples to bananas is $3:2$ , then we can let the numbers of apples and bananas equal $3n$ and $2n$ , respectively, for some positive integer $n$ .

Therefore, the total number of apples and bananas is $3n+2n = 5n$ , which is a multiple of 5.

Of the given choices, only (E) 72 is not a multiple of 5 and so cannot be the total.

(Each of the other choices can be the total by picking an appropriate value of $n$ .)

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.