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D01-04

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D01-04 [#permalink]

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New post 16 Sep 2014, 00:11
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Is \(x\) a prime integer?


(1) \(|x| = 2\)

(2) \(x^2 = 4\)
Spoiler: OA

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Re D01-04 [#permalink]

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New post 16 Sep 2014, 00:11
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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.


Answer: E
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Re: D01-04 [#permalink]

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New post 26 Nov 2014, 06:27
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.
Could someone please clarify
Thank you in advance

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Re: D01-04 [#permalink]

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New post 26 Nov 2014, 07:14
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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;
\(\sqrt[4]{16} = 2\), 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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Re: D01-04 [#permalink]

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New post 27 Nov 2014, 08:49
Thank you very much !

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Re: D01-04 [#permalink]

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New post 03 Dec 2014, 00:17
Don't we have negative primes?
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Re: D01-04 [#permalink]

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New post 03 Dec 2014, 04:28
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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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Re: D01-04 [#permalink]

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New post 29 Jun 2015, 01:00
(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..
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Re: D01-04 [#permalink]

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New post 14 May 2017, 02:24
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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Re: D01-04 [#permalink]

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New post 14 May 2017, 02:31
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: D01-04   [#permalink] 14 May 2017, 02:31
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