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


izzai

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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?

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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 Edited by BGPC Eliza
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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

 

Answer = A

 

Cheers,

Brent

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