Another approach to this

[oquiella]

88. If x is an integer, is x/2 an even integer?
(1) x is a multiple of 14
(2) x is a multiple of 126

Please simplify your explanation, the one below confuses me.


Explanation:
Statement 1: Let x = 14k, then x/2 = 7k, may be even or odd; NOT SUFFICIENT.
Statement 2: Let x = 126p, then x/2 = 63p; NOT SUFFICIENT.
Combining both the statements, the number which is divisible by 126 is always divisible by 14. Hence, same as statement 2, again NOT SUFFICIENT.
The correct answer is E;
both statements together are still not sufficient.

[GMATGuruNY]

88. If x is an integer, is x/2 an even integer?
(1) x is a multiple of 14
(2) x is a multiple of 126

Statement 1:
If x=14, then x/2 = 14/2 = 7, which is not an even integer.
If x=28, then x/2 = 28/2 = 14, which is an even integer.
INSUFFICIENT.

Statement 2:
If x=126, then x/2 = 126/2 = 63, which is not an even integer.
If x=252, then x/2 = 252/2 = 126, which is an even integer.
INSUFFICIENT.

Statements combined:
Since 126 = 14*9, any integer divisible by 126 is also divisible by 14.
Thus, the two values above that satisfy statement 2 -- 126 and 252 -- also satisfy satisfy statement 1.
In other words, x=126 and x=252 satisfy BOTH statements.
If x=126, then x/2 = 126/2 = 63, which is not an even integer.
If x=252, then x/2 = 252/2 = 126, which is an even integer.
INSUFFICIENT.

The correct answer is E.