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by imskpwr » Sat Sep 14, 2013 9:09 pm
If x2 is a positive integer, is x a positive integer?

(1)Sqrt x^2 is an integer.

(2)Sqrt x^2 = x
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
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by ani781 » Sun Sep 15, 2013 4:19 am
IMO answer is: B
Reason :
From(1)=> Sqrt x^2 is an integer.
Let x^2 = 16; then sqrt 16 = +4 or -4; ... so not sufficient.

From(2)=> sqrt x^2 = x; So clearly with the example taken from (1) the answer narrows down to only +4. Sufficient.
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by sanju09 » Sun Sep 15, 2013 5:07 am
imskpwr wrote:If x2 is a positive integer, is x a positive integer?

(1)Sqrt x^2 is an integer.

(2)Sqrt x^2 = x
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
I. When x = -2, √4 is 2 an integer, but x is not positive, hence NO. But, when x = 2, √4 is 2 an integer, and x is positive, hence YES. Insufficient. Get rid of A, D.

II. Square root of a positive number is always a positive number. Hence, if x^2 is a positive integer and √x^2 = x, x is definitely a positive integer. [spoiler]Sufficient

Choose B[/spoiler]
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by ani781 » Sun Sep 15, 2013 5:17 am
I. When x = -2, √4 is 2 an integer, but x is not positive, hence NO. But, when x = 2, √4 is 2 an integer, and x is positive, hence YES. Insufficient. Get rid of A, D.
Hi Sanju, I get it now , what was wrong with my understanding. Sqrt 16 can't be +4 or -4... it is only +4.

Thanks a lot for this.
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by Java_85 » Sun Sep 15, 2013 4:36 pm
IMO also B,
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