you are reading it the wrong way.
1. says X/2 is an integer that means X/2 = 1 or 2 or 3 etc. so X =2,4,6 etc. You can't assume X=1 because, they say X/2 is an integer which means X is even.
Let me know if this helps
Is X an integer?
1. X/2 is an integer
2.2x is an integer.
The answer is A.
I'm confused because the book states that according to 1, X would be an even integer and so that should make it sufficient. But why would that be true if when X=1, X/2=1/2? Or am I approaching it the wrong way?
yes it is important to make sure that you are clear about what the question is asking. Here (1) says that x divided by two is an integer, this means that x has to be an integer because it must be an even integer to mean that x/2 is an integer. (2) says that x multiplied by 2 is an integer that means that x could be an integer, like 1 or that it could not be like 1/2
Last edited by BGPC Eliza; 11-21-2014 at 10:09 AM.
Eliza Chute, GMAT Tutor
Statement 1: x/2 is an integer
In other words, x/2 = k, where k is an integer
Multiply both sides by 2 to get: x = 2k
In other words, x = (2)(some integer k)
If k is an integer, then x is an integer (an EVEN integer at that)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: 2x is an integer
There are several values of x that satisfy this condition. Here are two conflicting cases:
Case a: x = 1, in which case 2x = 2(1) = 2, and 2 is an integer. In this case, x IS an integer
Case b: x = 1.5, in which case 2x = 2(1.5) = 3, and 3 is an integer. In this case, x is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
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