Suppose $x$ is divisible by 8 but not by 3. Then which of the following CANNOT be an integer?

Answer Choices

Correct answer marked below

\frac{x}{2}

\frac{x}{4}

\frac{x}{6}

Correct

\frac{x}{8}

x

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Comments

RewantJun 7

Easy one — if x isn't divisible by 3, then dividing by 6 can never give an integer. Took me 20 seconds.

ShubhangiSep 23

Wait, why is (A) fine? Couldn't x be something like 8, so x/2 = 4, that works. But what if x were 16? Still fine. I think any multiple of 8 is even regardless.

MeenalMay 11

Could someone confirm the approach? I just picked x = 8 and tested each choice. Only the one with 6 failed. Is testing one value enough here since x is 'supposed' to be divisible by 8 but not 3?

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

Suppose xxx is divisible by 8 but not by 3. Then which of the following CANNOT be an integer?