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

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

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New post 24 Mar 2017, 00:31
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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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Re: If a is an integer, then the least possible value of |100-7a| is  [#permalink]

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New post 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.

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

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New post 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.

Answer: B.


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

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New post 27 Mar 2017, 17:23
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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.

Answer: B
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Re: If a is an integer, then the least possible value of |100-7a| is &nbs [#permalink] 27 Mar 2017, 17:23
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