If r is a negative integer, then what is the greatest possible value

Question

If r is a negative integer, then what is the greatest possible value of |12+4r|/r ?

a) -8
b) -4
c) 0 
d) 4
e) 8

IanStewart · Accepted Answer

An absolute value must be positive or zero, and r is negative. So we're dividing a positive number or zero by a negative number, and the result must either be negative or zero. Since the result can be equal to zero (when r = -3), that's the maximum possible value of the fraction.

GMATWhizTeam · Answer

Solution:  
We don't need to solve much in this question, we can answer this logically by making some pertinent inferences.
 •  |12+4r|  will always be non negative.
•  r  is a negative integer.
 o  \frac{|12+4r|}{r} , will either be negative or zero.
  We can eliminate Option D, and E 
o We know that zero is bigger than any negative number.
  So we just have to see, wheather for any of the value of r, the given expression can be zero or not.
 Or we can say  |12+4r|  can be zero or not. 
o If  r = -3 , then  |12+4r| = 0 .
  Which means the greatest value of  |12+4r|  is zero.   
Hence, the correct answer is  Option C.

udaypratapsingh99 · Answer

This is an easy, but tricky question. "r" in the denominator is the key element.

As r is negative(as given), the expression |12+4r|/r will always be negative because of denominator. Therefore, we need to try to get a value nearest to zero. Using r= -3, it becomes zero, therefore the answer is 0.

"Correct Answer is C"

BrushMyQuant · Answer

r is a negative integer and we need to find the greatest possible value of |12+4r|/r

Now, we know that  Absolute Value of a number is always non-negative

=> In  \frac{|12+4r|}{r} 
Numerator which is |12+4r| is non-negative and denominator which is r is negative

=> Maximum value of the number can be 0 only when numerator is 0
Which is when r = -3

So,  Answer will be C 
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

iamyogi25 · Answer

Why are we not solving like traditional approach i.e. -(12+4r)/r similar to |x|= -x case. Like other equations with absolute value cases: we check for both |x|=x and |x|=-x cases. I understand absolute values are always positive. But then why do we check |x|= -x case. I know I am missing something fundamental here. But what is it? Can somebody help? Thank you.

Bunuel · Answer

We are not solving an equation here. We are given an expression and asked to find the greatest possible value of that expression. The numerator, |12 + 4r|, is an absolute value, which is always positive or zero, while the denominator, r, is given to be negative. So we have something positive or zero divided by a negative number. That means the result can be either zero or negative. Since we are asked for the greatest value, the greatest value would be zero, when the numerator, |12 + 4r|, is 0, so when r = -3.

iamyogi25 · Answer

Thank you, Bunuel.

If r is a negative integer, then what is the greatest possible value

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If r is a negative integer, then what is the greatest possible value

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