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

Question

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

Bunuel · Accepted Answer

|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.

JeffTargetTestPrep · Answer

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

Bunuel · Answer

This is a copy of the following OG question: https://gmatclub.com/forum/if-y-is-an-i ... 39867.html

shuvodip04 · Answer

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.

MonkeyDDes · Answer

Instead '... the least...' with 'at least', the answer could be 'E'?

Posted from my mobile device

pratiksha1998 · Answer

We need to find the least possible value for |100-7a|:-

We know that the mod of any value results in a +ve value or a 0, therefore 100-7a>=0.
We know that a is an integer, so 100-7a cannot be 0 because for 100-7a to be 0 a will have to be equal to 100/7, which cannot be the case.

Now we have to solve for 100-7a>0
100>7a
7a<100
a<100/7
a at max can be 14
substituting a =14 in the equation,
100-7*14 => 100-98 => 2

Ans. 2

CrackverbalGMAT · Answer

Since a is an integer,we cannot have the least value as 0.

A thus is a "trap"!

Think of how close you could bring this value to 0, with a as an integer. Thus a must equal 12 so that |100-7a| = |100 - 7*12|=2

(option b)

D.S
GMAT SME

BrushMyQuant · Answer

Given that a is an integer and we need to find the least possible value of |100-7a|

Now, |100-7a| is Absolute Value/Modulus of a number and we know that Absolute Value of any number is always ≥ 0

=>  Minimum value of |100-7a| will be close to zero 
=> 100-7a should be close to 0

Since,  a  is an integer so let's take value of  a  in such a way that 100-7a is closer to 0
For a = 14
=> 100-7a = 100-7*14 = 100 - 98 = 2

For a = 15
=> 100-7a = 100-7*15 = 100 - 105 = -5

2 is closer to 0 than -5
=> Minimum value of |100-7a| = |2| = 2 (when a = 14)

So,  Answer will be B 
Hope it helps!

Watch the following video to learn How to Solve Absolute Value Problems

https://www.youtube.com/watch?v=rBWfl4AmQDI

bumpbot · Answer

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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

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