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Math Expert V
Joined: 02 Sep 2009
Posts: 58331

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Difficulty:   5% (low)

Question Stats: 77% (00:21) correct 23% (00:23) wrong based on 181 sessions

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Is $$x$$ a prime integer?

(1) $$|x| = 2$$

(2) $$x^2 = 4$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 58331

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Official Solution:

(1) $$|x|=2$$. So, $$x=2$$ or $$x=-2$$. Not sufficient.

(2) $$x^2=4$$. The same solution: $$x=2$$ or $$x=-2$$. Not sufficient.

(1)+(2) Nothing new: either $$x=2=prime$$ or $$x=-2\ne prime$$. Not sufficient.

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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 58331

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alexjordan99 wrote:
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

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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 $$x=\sqrt{9}=3$$.
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Thank you very much !

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Intern  Joined: 04 Apr 2012
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Location: India

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Don't we have negative primes?
Math Expert V
Joined: 02 Sep 2009
Posts: 58331

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harica wrote:
Don't we have negative primes?

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.
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(1) |x|=2 => x =+2 or x=-2.. NS

(2) x^2 = 4 = > |x| = 2 => x =+2 or x = -2 NS

On combining both mean the same.. Hence Not Sufficient.. Answer is E..
Intern  Joined: 11 Sep 2016
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In the above discussion it is said that we cannot have the negative prime so we will have only +2 as the answer and hence the answer should be d. please explain...
Math Expert V
Joined: 02 Sep 2009
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saaqibpatangiya wrote:
In the above discussion it is said that we cannot have the negative prime so we will have only +2 as the answer and hence the answer should be d. please explain...

Not sure what to explain there... Each statement gives TWO possible value of x: 2 and -2. The question asks whether x is a prime number. If x = 2, then YES x is a prime number but if x is -2, then NO x is NOT a prime number. We have two different answers to the question, thus not sufficient.

Hope it helps.
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Hi, sorry if this is a dumb question, but I thought the |x| signaled "absolute value" of a number? So even if you had a negative number it would still be a positive? 2 spots away from zero? So if x=2 then it would be enough information to answer whether x was a prime number? Does my question make sense?
Math Expert V
Joined: 02 Sep 2009
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ewatts wrote:
Hi, sorry if this is a dumb question, but I thought the |x| signaled "absolute value" of a number? So even if you had a negative number it would still be a positive? 2 spots away from zero? So if x=2 then it would be enough information to answer whether x was a prime number? Does my question make sense?

The question asks whether x is a prime number. (1) says that |x| = 2. So, x can be 2, which is prime or -2 which is NOT prime.
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