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# D01-04

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Math Expert
Joined: 02 Sep 2009
Posts: 51263

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15 Sep 2014, 23:11
00:00

Difficulty:

5% (low)

Question Stats:

77% (00:20) correct 23% (00:22) wrong based on 171 sessions

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Is $$x$$ a prime integer?

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

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

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Math Expert
Joined: 02 Sep 2009
Posts: 51263

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15 Sep 2014, 23:11
1
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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Intern
Joined: 03 Oct 2014
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26 Nov 2014, 05:27
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.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 51263

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26 Nov 2014, 06:14
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.

Posted from my mobile device

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;
$$\sqrt[4]{16} = 2$$, 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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27 Nov 2014, 07:49
Thank you very much !

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Joined: 04 Apr 2012
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02 Dec 2014, 23:17
Don't we have negative primes?
Math Expert
Joined: 02 Sep 2009
Posts: 51263

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03 Dec 2014, 03:28
2
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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Joined: 11 Apr 2014
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29 Jun 2015, 00:00
(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: 10 Sep 2016
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14 May 2017, 01:24
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...
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14 May 2017, 01:31
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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15 Sep 2018, 15:51
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
Joined: 02 Sep 2009
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16 Sep 2018, 00:16
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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Re: D01-04 &nbs [#permalink] 16 Sep 2018, 00:16
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# D01-04

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