Problem 31 Data Sufficiency OG Quant review 2nd edition

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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kso I was doing some problems in quant review second edition and I dont know if I am being stupid or if I came across a mistake.
The problem asks is (x)^1/2 an integer?
A) (4x)^1/2 is an integer
B) (3x)^1/2 is an integer

I know that B is insufficient, but I also think that A is insufficient yet A is the correct answer. Suppose (4x)^1/2=3 then you can pull out a 2 and you have (x)^1/2=3/2 or you can square both sides and you have 4x=9. either way it implies that x is equal to 9/4 which is not an integer. but if (4x)^1/2 = 2 then you have x is equal to 1 which is an integer.

To me this is evidence that both statements together are insufficient. However, the answer is that A is sufficient. Am I being totally stupid or does anyone else agree with my logic? If I am completely off what am I missing?
Source: — Quantitative Reasoning |

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by Brian@VeritasPrep » Thu Aug 26, 2010 1:02 pm
Hey, nice catch - I think you're right...unless the question somehow specifies that x is an integer, statement 1 doesn't work.

You can also look at it this way:

(4x)^1/2 = 4^1/2 * x ^ 1/2 = 2(x^1/2)

So we know that 2 * x^1/2 is an integer, but that allows x^1/2 to be 1/2, 3/2, 5/2, etc. Now, if x were an integer, then that would eliminate those options, but as long as x isn't specified that way 1 should really be insufficient.
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