If n is an integer, is n positive?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Jun 15, 2014 5:47 pm

Hello,

Can you please help with this:

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer
2) n = -n

OA: D

Thanks,
Sri

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 15, 2014 5:47 pm

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sun Jun 15, 2014 6:17 pm

gmattesttaker2 wrote:Hello,

Can you please help with this:

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer
2) n = -n

OA: D

Thanks,
Sri

n is an integer.

1) (2n+1)/(n+1) is an integer
(n+(n+1))/(n+1) is an integer.
n/(n+1) + 1 is an integer.
Lets remove the +1 as integer +1 is integer.
Adding +1 and -1 to the numerator;
((n+1)-1)/(n+1) is an integer.
1-1/(n+1) is an integer.
therefore 1/(n+1) is an integer.
To satisfy this condition 1/1 is the only integer possible. Hence n=0. (not positive)
Hence Statement1 is SUFFICIENT.

2) n=-n
2n=0
n=0
(not positive)
Hence Statement2 is SUFFICIENT.

Choose D

There might be easier ways to solve this. This would have been my first approach on the test.

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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
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by [email protected] » Sun Jun 15, 2014 6:40 pm

Hi Sri,

This DS question is perfect for TESTing Values; it also has some Number Properties built into it.

We're told that N is an integer. We're asked if N is positive. This is a YES/NO question.

Fact 1: (2N+1)/(N+1) = an integer.

Let's TEST VALUES:

If N = 0, we have 1/1 = an integer and the answer to the question is NO (because 0 is a "null" value; it is NOT positive).
If N = -2, we have -3/-1 = 3 = an integer and the answer to the question is NO.

When attempting to test a positive integer, we run into a problem....there are NO positive integers that satisfy Fact 1. N cannot be 1,2,3,4,5,etc., so we have no valid test cases that are positive. Based on the information that we DO have, the answer is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: N = -N

In the realm of math, there's only one solution to this equal. N must = 0 and the answer to the question is NO.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Wed Jun 07, 2017 6:23 pm, edited 1 time in total.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jun 15, 2014 6:50 pm

gmattesttaker2 wrote:Hello,

Can you please help with this:

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer
2) n = -n

Statement 1: (2n+1)/(n+1) is an integer
In other words, 2n+1 is a multiple of n+1.
If n>0, then the smallest possible multiple of n+1 -- after n+1 itself -- is as follows:
2(n+1) = 2n+2.
Thus, if n>0, it is not possible that 2n+1 -- a value LESS than 2n+2 -- is a multiple of n+1.
Implication:
n cannot be positive.
SUFFICIENT.

Statement 2: n=-n
Adding n to both sides, we get:
2n = 0
n = 0.
Thus, n is not positive.
SUFFICIENT.

The correct answer is D.

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AsadAbu: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Tue Oct 13, 2015 9:05 am

by AsadAbu » Wed Nov 23, 2016 9:38 pm

[email protected] wrote:
Fact 2: N = -N

In the realm of math, there's only one solution to this equal. N must = 0 and the answer to the question is NO.
Fact 2 is SUFFICIENT

Final Answer: B

But, my calculation says Statement 2 is not sufficient.
Statement 2:
n=-n
n+n=0
integer+integer=0
6+(-6)=0, (the summation of 2 integer will be zero if the integers are same value and carries opposite sign.
So, n=6,-6
---> not sufficient

adding the 2 statements:
The summation of 2 integer must be zero.
So, we can take these values as integer=6 and -6.
So, not sufficient.
Is there any mistake in my calculation?
thanks...

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AsadAbu: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Tue Oct 13, 2015 9:05 am

by AsadAbu » Wed Nov 23, 2016 10:10 pm

GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please help with this:

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer
2) n = -n
Statement 1: (2n+1)/(n+1) is an integer
In other words, 2n+1 is a multiple of n+1.
If n>0, then the smallest possible multiple of n+1 -- after n+1 itself -- is as follows:
2(n+1) = 2n+2.
Thus, if n>0, it is not possible that 2n+1 -- a value LESS than 2n+2 -- is a multiple of n+1.
Implication:
n cannot be positive.
SUFFICIENT.

Statement 2: n=-n
Adding n to both sides, we get:
2n = 0
n = 0.
Thus, n is not positive.
SUFFICIENT.

The correct answer is D.

Statement 1:
(2n+1)/(n+1)=integer
(2n+1)=integer (n+1)
(2n+1)=integer+integer
2n+1=integer
2n=integer-1
2n=integer-----equation (1)
So, if n=6, then equation (1)becomes...
2*6=integer
12=integer, which is ok.
again, if n=-6, then equation (1) becomes..
2*(-6)=integer
-12=integer, which is ok.

So, n=6,-6
---> not sufficient

Statement 2:
n=-n
n+n=0
integer+integer=0
6+(-6)=0, (the summation of 2 integer will be zero if the integers are same value and carries opposite sign.
So, n=6,-6
---> not sufficient

adding the 2 statements:
The summation of 2 integer must be zero.
So, we can take these values as integer=6 and -6.
So, not sufficient.
So, E to me.
is there any mistake in my calculation?

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by [email protected] » Thu Nov 24, 2016 8:05 am

Hi iMyself,

To start, you can double-check your calculations by plugging the 'solutions' that you've calculated back into the 'source equation' to make sure that they're actually solutions. In Fact 1, neither 6 nor -6 actually fits... so that should tell you that something is off in your work. In Fact 2, the equation uses just one variable: N; however, you rewrote that equation as integer + integer = 0, implying that the two integers could be different numbers. That is NOT possible though - the equation should be...

N+N = 0
2N = 0
N = 0

So N MUST be 0 (it can't be anything else).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Jan 16, 2017 9:10 pm

gmattesttaker2 wrote:Hello,

Can you please help with this:

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer
2) n = -n

OA: D

Thanks,
Sri

'n is an integer' mean that n is one among {..., -3, -2, -1, 0, 1, 2, 3, ...}

we have to see whether n is one among {1, 2, 3, ...}.

S1: (2n+1)/(n+1) is an integer

(2n+1)/(n+1) = [n+(n+1)]/(n+1) = n/(n+1) + 1

"'n/(n+1) + 1' is an integer" mean that 'n/(n+1)' is an integer.

We see that if we take n as positive, the denominator is more than the numerator by 1, making n/(n+1) a fraction < 1. Thus n cannot be positive. The answer is NO. A unique answer. Sufficient.

S2: n = -n

'n = -n' mean that a number is equal to its negative; it is not possible with any number except 0. Thus, n = 0 (Non-positive). The answer is NO. A unique answer. Sufficient.

Answer: D

-Jay
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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Jan 18, 2017 5:58 pm

Another approach:

S1:

(2n + 1) / (n + 1) =>

(n + (n + 1)) / (n + 1) =>

n/(n + 1) + (n + 1)/(n + 1) =>

n/(n + 1) + 1

We're told that's an integer, so n/(n + 1) must be an integer. But this is only possible if n = 0. So we know the sole value of n, SUFFICIENT.

S2:

n = -n

Add n to both sides:

2n = 0

So again, n = 0, SUFFICIENT.

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by Matt@VeritasPrep » Wed Jan 18, 2017 5:59 pm

n=-n
n+n=0
integer+integer=0
6+(-6)=0, (the summation of 2 integer will be zero if the integers are same value and carries opposite sign.
So, n=6,-6
---> not sufficient

adding the 2 statements:
The summation of 2 integer must be zero.
So, we can take these values as integer=6 and -6.
So, not sufficient.
Is there any mistake in my calculation?
thanks...

There is a mistake: you're letting n assume two different values in the same equation. (You can't have n be 6 and -6 simultaneously.) I like the idea though!

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rahul.sehgal@btgchampion: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Thu Mar 03, 2011 11:27 amFollowed by: 7 members; Location: New Delhi, India; Thanked: 3 times

by rahul.sehgal@btgchampion » Tue Jun 06, 2017 9:14 pm

Rich - Request you to correct the hidden answer as both the statements individually are SUFFICIENT. Thank you for your response to the question.

[email protected] wrote:Hi Sri,

This DS question is perfect for TESTing Values; it also has some Number Properties built into it.

We're told that N is an integer. We're asked if N is positive. This is a YES/NO question.

Fact 1: (2N+1)/(N+1) = an integer.

Let's TEST VALUES:

If N = 0, we have 1/1 = an integer and the answer to the question is NO (because 0 is a "null" value; it is NOT positive).
If N = -2, we have -3/-1 = 3 = an integer and the answer to the question is NO.

When attempting to test a positive integer, we run into a problem....there are NO positive integers that satisfy Fact 1. N cannot be 1,2,3,4,5,etc., so we have no valid test cases that are positive. Based on the information that we DO have, the answer is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: N = -N

In the realm of math, there's only one solution to this equal. N must = 0 and the answer to the question is NO.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Best Regards,
Rahul Sehgal

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Jun 07, 2017 6:24 pm

Hi Rahul,

Nice catch. I've fixed the issue.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: If n is an integer, is n positive?

by Brent@GMATPrepNow » Wed Jan 29, 2020 12:25 pm

gmattesttaker2 wrote: ↑
Sun Jun 15, 2014 5:47 pm
Hello,

Can you please help with this:

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer
2) n = -n

OA: D

Thanks,
Sri

Target question: Is n positive?

Given: In is an integer

Statement 1:(2n+1)/(n+1) is an integer
Rewrite as: (n+1+n)/(n+1) is an integer
Rewrite as: (n+1)/(n+1) + n/(n+1) is an integer
Or... 1 + n/(n+1) is an integer
This means that n/(n+1) is an integer
How can this be? How can some number divided by a number that's 1 greater be an integer?
This ONLY WORKS if n = 0, so statement 1 is really telling us that n = 0
In other words, n is NOT positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n=-n
Add n to both sides to get: 2n = 0
Divide both sides by 2 to get: n = 0
So, n is NOT positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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