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# If a is an integer, then the least possible value of |100-7a| is

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Joined: 28 May 2014
Posts: 518
GMAT 1: 730 Q49 V41
If a is an integer, then the least possible value of |100-7a| is  [#permalink]

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24 Mar 2017, 00:31
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25% (medium)

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68% (01:00) correct 32% (01:11) wrong based on 276 sessions

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If a is an integer, then the least possible value of |100-7a| is

(A) 0
(B) 2
(C) 5
(D) 98
(E) 107

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Math Expert
Joined: 02 Sep 2009
Posts: 56272
Re: If a is an integer, then the least possible value of |100-7a| is  [#permalink]

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24 Mar 2017, 01:10
saswata4s wrote:
If a is an integer, then the least possible value of |100-7a| is

(A) 0
(B) 2
(C) 5
(D) 98
(E) 107

|100-7a| represents the distance between 100 and 7a on the number line. Now, the distance will be minimized when 7a, which is multiple of 7, is closest to 100. Multiple of 7 which is closest to 100 is 98 (for a=14), so the least distance is 2: |100−98|=2.

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Re: If a is an integer, then the least possible value of |100-7a| is  [#permalink]

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24 Mar 2017, 01:12
Bunuel wrote:
saswata4s wrote:
If a is an integer, then the least possible value of |100-7a| is

(A) 0
(B) 2
(C) 5
(D) 98
(E) 107

|100-7a| represents the distance between 100 and 7a on the number line. Now, the distance will be minimized when 7a, which is multiple of 7, is closest to 100. Multiple of 7 which is closest to 100 is 98 (for a=14), so the least distance is 2: |100−98|=2.

This is a copy of the following OG question: https://gmatclub.com/forum/if-y-is-an-i ... 39867.html
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Re: If a is an integer, then the least possible value of |100-7a| is  [#permalink]

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27 Mar 2017, 17:23
2
saswata4s wrote:
If a is an integer, then the least possible value of |100-7a| is

(A) 0
(B) 2
(C) 5
(D) 98
(E) 107

Since we need to determine the least value of |100-7a|, we need to make 100 - 7a as close to zero as possible.

We see that if a = 14, then 7 x 14 = 98, which is the closest 7a will be to 100. Thus, the least possible value of |100-7a| is |100 - 98| = |2| = 2.

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Re: If a is an integer, then the least possible value of |100-7a| is  [#permalink]

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30 Dec 2018, 01:51
saswata4s wrote:
If a is an integer, then the least possible value of |100-7a| is

(A) 0
(B) 2
(C) 5
(D) 98
(E) 107

So here a can't be less than zero.
Because if a<0 then the value of the expression will increase.

if a=14 then |100 - 7*14| = |100-98| = 2 ,it is the least possible value.
Re: If a is an integer, then the least possible value of |100-7a| is   [#permalink] 30 Dec 2018, 01:51
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