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Is positive integer n – 1 a multiple of 3?

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Is positive integer n – 1 a multiple of 3? [#permalink] New post 04 Jun 2012, 10:51
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Question Stats:

40% (02:06) correct 60% (01:28) wrong based on 90 sessions
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3
[Reveal] Spoiler: OA
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Re: Is positive integer n – 1 a multiple of 3? [#permalink] New post 04 Jun 2012, 11:15
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ShreeCS wrote:
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3


Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> n^3-n=n(n^2-1)=(n-1)n(n+1)=3q. Now, n-1, n, and n+1 are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 --> n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p --> so either n or n+1 is a multiple of 3, as out of 3 consecutive integers n-1, n, and n+1 only one is a multiple of 3 then knowing that it's either n or n+1 tells us that n-1 IS NOT multiple of 3. Sufficient.

Answer: B.
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Re: Is positive integer n – 1 a multiple of 3? [#permalink] New post 12 Sep 2012, 05:17
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Bunuel wrote:
ShreeCS wrote:
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3


Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> n^3-n=n(n^2-1)=(n-1)n(n+1)=3q. Now, n-1, n, and n+1 are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 --> n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p --> so either n or n+1 is a multiple of 3, as out of 3 consecutive integers n-1, n, and n+1 only one is a multiple of 3 then knowing that it's either n or n+1 tells us that n-1 IS NOT multiple of 3. Sufficient.

Answer: B.


Hi Bunuel,
I got a question. "Is positive integer n-1 a multiple of 3" doesn't require a specific answer?
Through the Statement 2 we figure out that n-1 is a multiple of 3 only if n+1 would be as well, and the answer is yes, conversely if n would be a multiple of 3, in this case the answer is no.
Could me please explain better this doubt
Thank you
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Re: Is positive integer n – 1 a multiple of 3? [#permalink] New post 12 Sep 2012, 05:29
1
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KUDOS
Expert's post
mario1987 wrote:
Bunuel wrote:
ShreeCS wrote:
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3


Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> n^3-n=n(n^2-1)=(n-1)n(n+1)=3q. Now, n-1, n, and n+1 are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 --> n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p --> so either n or n+1 is a multiple of 3, as out of 3 consecutive integers n-1, n, and n+1 only one is a multiple of 3 then knowing that it's either n or n+1 tells us that n-1 IS NOT multiple of 3. Sufficient.

Answer: B.


Hi Bunuel,
I got a question. "Is positive integer n-1 a multiple of 3" doesn't require a specific answer?
Through the Statement 2 we figure out that n-1 is a multiple of 3 only if n+1 would be as well, and the answer is yes, conversely if n would be a multiple of 3, in this case the answer is no.
Could me please explain better this doubt
Thank you


In a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

The question asks whether n-1 is a multiple of 3, and from (2) we have a definite NO answer to this question, so this statement is sufficient.

Hope it's clear.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Math Expert
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Posts: 17321
Followers: 2875

Kudos [?]: 18405 [0], given: 2350

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Re: Is positive integer n – 1 a multiple of 3? [#permalink] New post 21 Aug 2013, 02:15
Expert's post
Re: Is positive integer n – 1 a multiple of 3?   [#permalink] 21 Aug 2013, 02:15
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