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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8013
GMAT 1: 760 Q51 V42 GPA: 3.82
If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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16 00:00

Difficulty:   45% (medium)

Question Stats: 64% (01:30) correct 36% (01:27) wrong based on 564 sessions

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If a, b are integers and |a-b|=8, which of the following is the smallest possible value of ab?
A. -16
B. 0
C. 16
D. 7
E. 40

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Intern  B
Joined: 25 Jan 2016
Posts: 9
Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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1
The value will be lowest when a= -4 and b= 4--> | -4 - 4| = 8
(an)min = 4*-4 = -16
Hence A.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8013
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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a=4, b=-4. Hence, the answer is A.
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Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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Why is the answer not 0? If a=8 and b=0?
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1428
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Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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yk510 wrote:
Why is the answer not 0? If a=8 and b=0?

Hi

The question asks, "What is the smallest possible value of a*b?"

Like you, when I read the question, I also noticed that getting '0' is easy: take a=8 and b=0. But then I saw that there is another option given which is less than 0 (which is -16). So we have to check whether -16 is also possible or not, since the question asks for lowest value possible.

So with some trial/error, I saw that indeed -16 is possible when I take a=-4 and b=4. because |-4-4| = |-8| = 8, and -4*4 = 16.
Senior PS Moderator V
Joined: 26 Feb 2016
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Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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1
In min-max expression questions,
we have to take the maximum value of one integer
and a minimum value of another integer which satisfy the equation
Since the expression is |a-b| = 8
the range of this expression must be -8 <= a - b <= 8

This is possible when a=-4 and b=4 or a=4,b=-4
In either case, ab = -16(Option A)
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Joined: 23 May 2016
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Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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yk510 wrote:
Why is the answer not 0? If a=8 and b=0?

When you convert this expression to liner equation it is a+(-b) = 8 when a>b or a + (-b) = -8 when a<b.

So, now if you see the values of a and b for which the product wil be minimum when corresponding values are 4 and -4 and hence the product = -16. Hope this makes sense
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Re: If a, b are integers and |a-b|=8, which of the following is the smalle  [#permalink]

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_________________ Re: If a, b are integers and |a-b|=8, which of the following is the smalle   [#permalink] 21 Jan 2019, 09:35
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