# Thread: Easy data sufficiency question that's confusing. OG 12th ed

1. ## Easy data sufficiency question that's confusing. OG 12th ed

Is X an integer?
1. X/2 is an integer
2.2x is an integer.

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?  Reply With Quote

2. izzai:

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   Reply With Quote

3. It does! Thank you!  Reply With Quote

Agree with a

Put in x= 1,1/2,3/2,2, only first statement satisfies  Reply With Quote

5. 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  Reply With Quote

6. Originally Posted by izzai Is x an integer?
1) x/2 is an integer
2) 2x is an integer.
Target question:Is x an integer?

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

Cheers,
Brent  Reply With Quote