If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. (True or False)

True

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False

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Solution

The correct option is B False
If a number exactly divides the sum of two numbers, it doesn't exactly divide the two numbers separately.
To prove the given statement is false we give a counter example
Counter example : $27$ is exactly divided by $3$ , so, we can write it as,
$27 = 14 + 13$
Now, $3$ does not divide either $14$ or $13$ exactly.
Hence, from the counter example it is proven that the given statement is false.

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