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Is OG Quant question answer wrong?

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Is OG Quant question answer wrong? [#permalink] New post 20 Feb 2010, 14:49
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Question Stats:

25% (01:09) correct 75% (00:41) wrong based on 0 sessions
This is the question from GMAT Quant Review:

If x is a positive integer , is \sqrt{x} an integer?

(1) \sqrt{4x} is an integer.
(2) \sqrt{3x} is not an integer.

My logic to solve this question:

\sqrt{4x}=2*\sqrt{x}, so \sqrt{x} can either be integer or not an integer (for example \sqrt{x}=2.5) and the 2*\sqrt{x} is still an integer. So Statement 1 is insufficient.

\sqrt{3x}= \sqrt{3}*\sqrt{x}. As \sqrt{3} is not an integer, the \sqrt{x} can be either integer or non integer and the \sqrt{3}*\sqrt{x} will still be not integer. So Statement 2 is insufficient.

S1 and S2 together is still insufficient as \sqrt{x}=2 and \sqrt{x}=2.5 both satisfy statements requirement.

So I choose E as an answer.

Is there a flaw in my reasoning? OG Quant review answer to this question is different from E.
Please advice.
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Re: Is OG Quant question answer wrong? [#permalink] New post 20 Feb 2010, 15:14
alexBLR wrote:
This is the question from GMAT Quant Review:

If x is a positive integer , is \sqrt{x} an integer?

1) \sqrt{4x} is an integer.
2) \sqrt{3x} is not an integer.

My logic to solve this question:

\sqrt{4x}=2*\sqrt{x}, so \sqrt{x} can either be integer or not an integer (for example \sqrt{x}=2.5) and the 2*\sqrt{x} is still an integer. So Statement 1 is insufficient.

\sqrt{3x}= \sqrt{3}*\sqrt{x}. As \sqrt{3} is not an integer, the \sqrt{x} can be either integer or non integer and the \sqrt{3}*\sqrt{x} will still be not integer. So Statement 2 is insufficient.

S1 and S2 together is still insufficient as \sqrt{x}=2 and \sqrt{x}=2.5 both satisfy statements requirement.

So I choose E as an answer.

Is there a flaw in my reasoning? OG Quant review answer to this question is different from E.
Please advice.


IMO D...

Ques: if x is a positive integer, is \sqrt{x} an integer?

S1: \sqrt{4x} is an integer

--> 2* \sqrt{x} is an integer --> \sqrt{x} has to be an integer.. as x is a positive integer and hence cannot be a fraction. Therefore SUFF

S2: \sqrt{3x} is an integer
--> \sqrt{3}*\sqrt{x} --> \sqrt{x} is not an integer as same could be a of a form of a\sqrt{3} where 'a' is a positive integer. Therefore SUFF
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Re: Is OG Quant question answer wrong? [#permalink] New post 20 Feb 2010, 15:57
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jeeteshsingh wrote:
alexBLR wrote:
This is the question from GMAT Quant Review:

If x is a positive integer , is \sqrt{x} an integer?

1) \sqrt{4x} is an integer.
2) \sqrt{3x} is not an integer.

My logic to solve this question:

\sqrt{4x}=2*\sqrt{x}, so \sqrt{x} can either be integer or not an integer (for example \sqrt{x}=2.5) and the 2*\sqrt{x} is still an integer. So Statement 1 is insufficient.

\sqrt{3x}= \sqrt{3}*\sqrt{x}. As \sqrt{3} is not an integer, the \sqrt{x} can be either integer or non integer and the \sqrt{3}*\sqrt{x} will still be not integer. So Statement 2 is insufficient.

S1 and S2 together is still insufficient as \sqrt{x}=2 and \sqrt{x}=2.5 both satisfy statements requirement.

So I choose E as an answer.

Is there a flaw in my reasoning? OG Quant review answer to this question is different from E.
Please advice.


IMO D...

Ques: if x is a positive integer, is \sqrt{x} an integer?

S1: \sqrt{4x} is an integer

--> 2* \sqrt{x} is an integer --> \sqrt{x} has to be an integer.. as x is a positive integer and hence cannot be a fraction. Therefore SUFF

S2: \sqrt{3x} is an integer
--> \sqrt{3}*\sqrt{x} --> \sqrt{x} is not an integer as same could be a of a form of a\sqrt{3} where 'a' is a positive integer. Therefore SUFF


As given that x is a positive integer then \sqrt{x} is either an integer itself or an irrational number.

(1) \sqrt{4x} is an integer --> 2\sqrt{x}=integer --> 2\sqrt{x} to be an integer \sqrt{x} must be an integer or integer/2, but as x is an integer, then \sqrt{x} can not be integer/2, hence \sqrt{x} is an integer. Sufficient.

(2) \sqrt{3x} is not an integer --> if x=9, condition \sqrt{3x}=\sqrt{27} is not an integer satisfied and \sqrt{x}=3 IS an integer, BUT if x=2, condition \sqrt{3x}=\sqrt{6} is not an integer satisfied and \sqrt{x}=\sqrt{2} IS NOT an integer. Two different answers. Not sufficient.

Answer: A.

jeeteshsingh, you should have spotted that there was something wrong with your solution as in DS two statements can not give you TWO DIFFERENT answers to the question (as you've got).

Hope it helps.
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Re: Is OG Quant question answer wrong? [#permalink] New post 20 Feb 2010, 16:13
Bunuel wrote:
jeeteshsingh, you should have spotted that there was something wrong with your solution as in DS two statements can not give you TWO DIFFERENT answers to the question (as you've got).

Hope it helps.


:wall My Bad.... overlooked it... Infact today I was telling this to someone over the forum that both the statements in DS would always be in sync..

Thanks Bunuel... for pointing this out.
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Re: Is OG Quant question answer wrong? [#permalink] New post 20 Feb 2010, 16:42
When I assumed the case \sqrt{x}=2.5 I did not take into the account that x will not be an integer in this case(x=6.25). Thanks Bunuel
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Integers [#permalink] New post 28 Feb 2011, 12:43
If x is positive integer, is \sqrt{x} an integer?
1) \sqrt{4x} is an integer
2) \sqrt{3x} is not an integer
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Re: Integers [#permalink] New post 28 Feb 2011, 12:56
Merging similar topics.

Similar questions:
if-x-is-a-positive-integer-is-sqrt-x-an-integer-88994.html
value-of-x-107195.html
number-prop-ds-106886.html
number-system-106606.html
odd-vs-even-trick-question-106562.html
quant-review-2nd-edition-ds-104421.html
algebra-ds-101464.html
quant-review-2nd-edition-ds-104421.html
q-31-og-12-ds-101918.html
airthmetic-ds-108287.html

Hope it helps.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: Integers   [#permalink] 28 Feb 2011, 12:56
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