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# If n is an integer, then the least possible value of l31 - 4nl is

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Manager
Joined: 18 Feb 2015
Posts: 82
If n is an integer, then the least possible value of l31 - 4nl is  [#permalink]

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05 Jul 2016, 11:55
3
4
00:00

Difficulty:

15% (low)

Question Stats:

69% (00:45) correct 31% (00:58) wrong based on 384 sessions

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If n is an integer, then the least possible value of |31 - 4n| is?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

GMAT Total Maths
Math Expert
Joined: 02 Sep 2009
Posts: 56300
Re: If n is an integer, then the least possible value of l31 - 4nl is  [#permalink]

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05 Jul 2016, 12:07
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2
HarveyKlaus wrote:
Hi All;

I found this question in GMAT Total Maths, but Im not able to understand the solution provided. Would appreciate if someone could please comment? Thanks

If n is an integer, then the least possible value of |31 - 4n| is?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

|31 - 4n| represents the distance between 31 and 4n on the number line. Now, the distance will be minimized when 4n, which is multiple of 4, is closest to 31. Multiple of 4 which is closest to 31 is 32 (for n = 8), so the least distance is 1: |31 - 32| = 1.

Hope it's clear.
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Schools: Schulich '16
Re: If n is an integer, then the least possible value of l31 - 4nl is  [#permalink]

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05 Jul 2016, 22:54
when modulus questions are there think about DISTANCE and modulus is always absolute value i.e positive

|31-4n|

so the minimum would be when n=8..the distance would be the least from 31 i.e.1

don't worry abut -ve or +ve value inside the modulus.coz mod is always +ve

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Re: If n is an integer, then the least possible value of l31 - 4nl is  [#permalink]

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09 Mar 2018, 09:25
HarveyKlaus wrote:
If n is an integer, then the least possible value of |31 - 4n| is?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

GMAT Total Maths

Please note that question is not asking the least value of "n".

32 is the closest integer to 31 which we can get by multiplying 4*8.

Therefore, |31 - 4*8| = 1

Hence, (B)
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Re: If n is an integer, then the least possible value of l31 - 4nl is   [#permalink] 09 Mar 2018, 09:25
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