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If a, b are integers and |a-b|=8

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If a, b are integers and |a-b|=8

by Vincen » Mon Sep 25, 2017 6:28 pm
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

The OA is B.

If we set a=4 and b=-4, then |a-b|=|4+4|=8. And ab=-16. Why is B the correct option?
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by Jay@ManhattanReview » Mon Sep 25, 2017 9:16 pm
Vincen wrote: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

The OA is B.

If we set a=4 and b=-4, then |a-b|=|4+4|=8. And ab=-16. Why is B the correct option?
Hi Vincen,

Your answer is correct.

ab is minimum if a = 4 and b = -4 OR a = -4 and b = 4. Option B (0) is correct if it were given that a and b are non-negative integers.

The correct answer: A

Hope this helps!

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by Matt@VeritasPrep » Tue Sep 26, 2017 5:14 pm
You're correct, -16 is the minimum. (Proving that is a bit more complicated, but with these answer choices we don't really need the proof.)

Either the OA is a typo or the stem itself is missing some qualifier.
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by Scott@TargetTestPrep » Thu Jan 18, 2018 7:59 am
Vincen wrote: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
The smallest possible value of ab is the one in which a and b have opposite signs. In that case, the value of ab must be negative since positive x negative = negative. The only negative value given in the answer choices is A, -16. Thus, A is the correct answer.

Answer: A

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by DrMaths » Thu Jan 18, 2018 8:12 am
You are perfectly correct for the reason you gave.
To have an answer of zero, the question would have to ask for POSITIVE integers.
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