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# If n is a positive integer, which of the following must be divisible

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Senior Manager
Joined: 18 Feb 2019
Posts: 380
Location: India
GMAT 1: 460 Q42 V13
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If n is a positive integer, which of the following must be divisible  [#permalink]

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22 Mar 2019, 23:19
1
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:37) correct 69% (02:45) wrong based on 59 sessions

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If n is a positive integer, which of the following must be divisible by 12?

I. n^4–n^2
II. (n-6)^2(n-4)(n+13)^2
III. 2n(n-10)(n+13)

A. I and II only
B. II and III only
C. I and III only
D. I, II and III
E. None of the above
CEO
Joined: 18 Aug 2017
Posts: 3533
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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26 Mar 2019, 10:01
kiran120680 wrote:
If n is a positive integer, which of the following must be divisible by 12?

I. n^4–n^2
II. (n-6)^2(n-4)(n+13)^2
III. 2n(n-10)(n+13)

A. I and II only
B. II and III only
C. I and III only
D. I, II and III
E. None of the above

take n = 2 and check with each options
we observe that all options are correct
IMO D
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Manager
Joined: 03 May 2013
Posts: 67
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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27 Mar 2019, 19:21
It's must be, not should be, oa is A

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Manager
Joined: 11 Aug 2017
Posts: 57
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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28 Mar 2019, 03:37
Archit3110 wrote:
kiran120680 wrote:
If n is a positive integer, which of the following must be divisible by 12?

I. n^4–n^2
II. (n-6)^2(n-4)(n+13)^2
III. 2n(n-10)(n+13)

A. I and II only
B. II and III only
C. I and III only
D. I, II and III
E. None of the above

take n = 2 and check with each options
we observe that all options are correct
IMO D

If one value proofs the statement correct for all , does that mean any value will satisfy the stem.??

CEO
Joined: 18 Aug 2017
Posts: 3533
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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28 Mar 2019, 03:38
1
Archit3110 wrote:
kiran120680 wrote:
If n is a positive integer, which of the following must be divisible by 12?

I. n^4–n^2
II. (n-6)^2(n-4)(n+13)^2
III. 2n(n-10)(n+13)

A. I and II only
B. II and III only
C. I and III only
D. I, II and III
E. None of the above

take n = 2 and check with each options
we observe that all options are correct
IMO D

If one value proofs the statement correct for all , does that mean any value will satisfy the stem.??

not necessarliy always ... its best to check upto 4 values..
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Intern
Joined: 22 Sep 2018
Posts: 9
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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30 Mar 2019, 06:05
1
kiran120680 wrote:
If n is a positive integer, which of the following must be divisible by 12?

I. n^4–n^2
II. (n-6)^2(n-4)(n+13)^2
III. 2n(n-10)(n+13)

A. I and II only
B. II and III only
C. I and III only
D. I, II and III
E. None of the above

which of the following "must be" not definitely .so substitute random numbers in the

I. n^4–n^2: n^2(n-1)(n+1)

take n = 4

4^2 * 3 * 5.....it is divisible by 12

(n-6)^2(n-4)(n+13)^2

take n = 12

6^2*2*19.......divisible by 12

2n(n-10)(n+13)

take n =12

2*12*2*25......divisible by 12

so the answer is all three...option:D
Intern
Joined: 07 Jan 2014
Posts: 12
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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31 Mar 2019, 08:42
The first option of n^4-n^2 becomes invalid if we take n=1 which staisfies the condition of n being a positive integer. The answer then should be B) II & III only.

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Manager
Joined: 31 Oct 2018
Posts: 78
Location: India
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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31 Mar 2019, 21:21
deushyant Zero is divisible by any no. except 0. 0/n = 0. n ={any no. except zero}

deushyant wrote:
The first option of n^4-n^2 becomes invalid if we take n=1 which staisfies the condition of n being a positive integer. The answer then should be B) II & III only.

Posted from my mobile device

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Manager
Joined: 23 Jan 2018
Posts: 164
Location: India
WE: Information Technology (Computer Software)
Re: If n is a positive integer, which of the following must be divisible  [#permalink]

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07 Apr 2019, 00:13
Is there any algebraic method to check 2nd and 3rd choice ?

Regards,
Arup
Re: If n is a positive integer, which of the following must be divisible   [#permalink] 07 Apr 2019, 00:13
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