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

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Nums99
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If r is a negative integer, then what is the greatest possible value [#permalink] New post   Updated on: 29 Jul 2019, 05:09
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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
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C

Originally posted by Nums99 on 29 Jul 2019, 05:07.
Last edited by Bunuel on 29 Jul 2019, 05:09, edited 1 time in total.
Renamed the topic.
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Re: If r is a negative integer, then what is the greatest possible value [#permalink] New post   29 Jul 2019, 08:33
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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.
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Re: If r is a negative integer, then what is the greatest possible value [#permalink] New post   20 Feb 2020, 01:25
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Nums99 wrote:
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

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.
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Re: If r is a negative integer, then what is the greatest possible value [#permalink] New post   28 Feb 2021, 04:55
Nums99 wrote:
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



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"
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Re: If r is a negative integer, then what is the greatest possible value [#permalink]
28 Feb 2021, 04:55
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