Is x an integer? (1) x/2 is an integer (2) 2x is an integer

Is x an integer?

(1) x/2 is an integer. For x/2 to be an integer x must be an integer --> \(\frac{x}{2}=integer\) --> \(x=2*integer=integer\), as you can see \(x\) is not only an integer but an even integer. Sufficient.

(2) 2x is an integer --> x may or may not be an integer, for instance \(x=0.5\) or \(x=1\). Basically \(x\) is of a type \(\frac{integer}{2}\), hence \(x\) may be an integer itself or half of an integer 0.5, 1.5, ... Not sufficient.

Answer: A.

As for your example: 4/2=2=integer, so 4/2 is just another way of writing integer 2, like 6/3 or 8/4. Also notice that any integer can be expressed as the ratio of 2 integers.

Hope it's clear.
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Is x an integer?

(1) x/2 is an integer if its decimal / will leave a decimal -S
(2) 2x is an integer-NS

For these integer questions, we can always set the integer equal to \(i\), where \(i\) represents any integer (or positive integer to test values).

Statement 1:
\(x/2 = i\), \(x = 2*i\). Thus x is double of any integer, which is still an integer. Then x must be an integer. Sufficient.

Statement 2:
\(2x = i\), \(x = i/2\). Thus x is half of any integer, which doesn't always result in an integer. Then x isn't always an integer, insufficient.

Ans: A
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