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If n is a positive integer and r is the remainder when n^2 - 1 is

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If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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New post 21 Jan 2012, 18:04
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If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

(1) n is odd
(2) n is not divisible by 8



As the OA is not provided this is how I solved this. Please let me know whether I am right or not.

Considering Statement 1

n =1 then remainder will be zero. ----------------> Is my thinking correct over here? If it is then for me this statement is sufficient to answer the question.

Considering statement 2

There will be different values for r and therefore its insufficient.

Therefore, for me the answer should be A unless someone has any other ideas. Please help.

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

n^2-1=(n-1)(n+1)

(1) n is odd --> both n-1 and n+1 are even. Moreover, they are consecutive even integers thus one of them is divisible by 4 too. Now, as one is divisible by 2 and another by 4 then (n-1)(n+1) is divisible by 2*4=8. Sufficient.

(2) n is not divisible by 8 --> try n=1 to get an YES answer and n=2 to get a NO answer. Not sufficient.

Answer: A.
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Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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New post 21 Jan 2012, 18:45
enigma123 wrote:
If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?
1). n is odd
2). n is not divisible by 8

As the OA is not provided this is how I solved this. Please let me know whether I am right or not.

Considering Statement 1

n =1 then remainder will be zero. ----------------> Is my thinking correct over here? If it is then for me this statement is sufficient to answer the question.

Considering statement 2

There will be different values for r and therefore its insufficient.

Therefore, for me the answer should be A unless someone has any other ideas. Please help.


As you can see from my post above answer is indeed A. But you arrived to A while trying only one value for n, which is not enough. For some other question, different values could give different answers and a statement would be insufficient in that case. What I mean is, when you decide that a statement is sufficient based only on plug-in method you should make sure that you tried several different numbers (and saw some pattern maybe), and even in this case you may not be 100% sure that the answer would be correct. Though if several numbers give the same answer and you are able to see some pattern, then you can make an educated guess that a statement is sufficient and move-on.

Generally on DS questions when plugging numbers, your goal is to prove that the statement is not sufficient. So you should try to get an YES answer with one chosen number(s) and a NO with another.

Hope it's clear.
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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

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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Director
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Status: Finally Done. Admitted in Kellogg for 2015 intake
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Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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New post 24 Jan 2012, 18:07
Bunuel - its clear apart from one minor doubt. In statement 1 why can't we take n =1 ?
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MGMAT 1 --> 530
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GMAT ==> 730

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Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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New post 24 Jan 2012, 18:19
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enigma123 wrote:
Bunuel - its clear apart from one minor doubt. In statement 1 why can't we take n =1 ?


Actually we can. Solution above does not exclude this possibility: n=1=odd then n^2-1=0 and zero is divisible by any integer (except zero itself), so it's divisible by 8 too. Sufficient.

The point is that you arrived that (1) is sufficient based only on one value of n, n=1. And as I discussed above one value is not enough to conclude that the statement is sufficient.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
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Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 514
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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New post 24 Jan 2012, 18:24
Oh yes. Entirely agree. Many thanks again.
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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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New post 26 Dec 2016, 07:49
1). N is odd, then n=2k+1, n^2 - 1=(2k+1)^2-1=4k^2+4k=4k(k+1). One of k and k+1 must be even, therefore, 4k(k+1) is divisible by 8.
Answer is A
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Re: If n is a positive integer and r is the remainder when n^2 - 1 is [#permalink]

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Re: If n is a positive integer and r is the remainder when n^2 - 1 is   [#permalink] 27 Jan 2018, 08:14
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