Maths Olympiad Prep

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, 2022

Number theory Difficulty 1.1 Junior Find the answer Canada

The integer 119 is a multiple of

Pick one

Solution

The ones digit of 119 is not even, so 119 is not a multiple of
2.

The ones digit of 119 is not 0 or 5, so 119 is not a multiple of
5.

Since 120=3×40120 = 3 \times 40, then 119
is 1 less than a multiple of 3 so is not itself a multiple of 3.

Since 110=11×10110 = 11 \times 10 and 121=11×11121 = 11 \times 11, then 119 is between
two consecutive multiples of 11, so is not itself a multiple of
11.

Finally, 119÷7=17119 \div 7 = 17, so 119 is
a multiple of 7.

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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.