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Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an

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Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink] New post 31 Aug 2010, 13:04
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Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Apr 2012, 02:48, edited 1 time in total.
Edited the question and added the OA
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Re: N [#permalink] New post 31 Aug 2010, 13:18
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Expert's post
vwjetty wrote:
Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer

Please explain. Thanks.


Is n an integer?

(1) n^2 is an integer --> not sufficient, as if n^2=4 answer is YES, but if n^2=3 answer is NO.

(2) n^(1/2) is an integer --> \sqrt{n}=integer --> n=integer^2=integer. Sufficient.

Answer: B.
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Re: N [#permalink] New post 31 Aug 2010, 13:20
oh wow. i feel dumb now. for some reason i was thinking something else. tricky tricky. thx. +1 kudo's good sir.
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Re: OG 11th edition [#permalink] New post 12 Dec 2011, 12:31
Answer is indeed B.

stmt 1: says that n^2 is an integer. So n could be 4, which n^16 or n could be 5.477 and n^2 would be 30. This gives us two different options so insuff

stmt 2: says that sqrt n is an integer. that means n is the square of an (or integer x integer) which will always give you an integer. suff
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Re: OG 11th edition [#permalink] New post 23 Dec 2011, 00:16
Is n an integer?

(1) n^2 is an integer

(2) sqrt(n) is an integer

S1: If n^2 is an integer, is n an integer?

Is n rational or irrational?

If rational, then n can be expressed as p/q,
where p and q are non-zero integers.
Further, if n^2 = (p/q)^2 is an integer, n = p/q is an integer.

If irrational, then n could be the non-integer square root of an integer, whose square is an integer.

S2: An integer multiplied by another integer is an integer.
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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink] New post 05 Apr 2012, 03:31
Thank you for the explanations. I know have an understanding of the question.
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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink] New post 20 Jun 2013, 14:07
Stament 1 : n^2=integer
n=+/- sqrt(integer)
=> Sqrt of integer may or may not be integer depending on whether chose integer is perfect square
or not. insufficient

Statement 2: sqrt (n) = integer
=> Squaring both sides
=> n= integer^2 = some other integer (as intg*intg=intg)
= sufficient

Ans B
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Re: N [#permalink] New post 30 May 2014, 01:27
Bunuel wrote:
vwjetty wrote:
Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer

Please explain. Thanks.


Is n an integer?

(1) n^2 is an integer --> not sufficient, as if n^2=4 answer is YES, but if n^2=3 answer is NO.

(2) n^(1/2) is an integer --> \sqrt{n}=integer --> n=integer^2=integer. Sufficient.

Answer: B.


If we take \sqrt{3} = 1.732050807568877
and square it, we still get 2.999999999999
which is not an integer. That's the reason I marked D :( :roll:

Last edited by b2bt on 30 May 2014, 03:59, edited 1 time in total.
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Re: N [#permalink] New post 30 May 2014, 02:21
Expert's post
b2bt wrote:
Bunuel wrote:
vwjetty wrote:
Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer

Please explain. Thanks.


Is n an integer?

(1) n^2 is an integer --> not sufficient, as if n^2=4 answer is YES, but if n^2=3 answer is NO.

(2) n^(1/2) is an integer --> \sqrt{n}=integer --> n=integer^2=integer. Sufficient.

Answer: B.


If we take \sqrt{3} = 1.732050807568877
and square it, we still get 2.999999999999
which is not an integer. That's the reason I marked D :( :roll:


Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 Please read.

\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806.... It's an irrational number, it goes on forever. Anyway, what's your question?
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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., 11 New DS set.


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Re: N [#permalink] New post 30 May 2014, 03:54
Quote:

Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 Please read.

\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806.... It's an irrational number, it goes on forever. Anyway, what's your question?


How can square of non-integer be an integer?
1.73 is a non- integer and so is its square
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Re: N [#permalink] New post 30 May 2014, 04:06
Expert's post
b2bt wrote:
Quote:

Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 Please read.

\sqrt{3}=1.732050807568877293527446341505872366942805253810380628055806.... It's an irrational number, it goes on forever. Anyway, what's your question?


How can square of non-integer be an integer?
1.73 is a non- integer and so is its square


The square root of 3 is a number which when squared gives 3.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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., 11 New DS set.


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Re: N   [#permalink] 30 May 2014, 04:06
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