D01-04

Question

Is  x  a prime integer?

(1)  |x| = 2 
 
(2)  x^2 = 4

Bunuel · Answer

Official Solution:

Is  x  a prime integer? 
 
(1)  |x|=2 . 
 
This statement implies that  x = 2  (which is prime) or  x = -2  (which is not prime). Not sufficient.
 
(2)  x^2=4 . 
 
This statement leads to the same solution:  x = 2  or  x = -2 . Not sufficient.
 
(1) + (2) We still have either  x = 2  (which is prime) or  x = -2  (which is not prime). Not sufficient.

Answer: E

alexjordan99 · Answer

Hi all
I thought that when you took the square root of a perfect square you only needed to consider the positive answer for GMAT questions so in this case the answer would be B. 
Could someone please clarify
Thank you in advance

Posted from my mobile device

Bunuel · Answer

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root.  That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2;

Notice that in contrast, the equation  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

harica · Answer

Don't we have negative primes?

Bunuel · Answer

No, by definition only positive integers can be primes. Check below links. Theory on Number Properties: math-number-theory-88376.html Tips on Number Properties: number-properties-tips-and-hints-174996.html Hope it helps.

FALSEnine · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Phillipe · Answer

Hi, I can't see what the options a, b, c, d and e are. It is not showing in this exercise.

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

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