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If a and b are integers and |a - b| = 16, what is the minimum possible

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If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 16 Apr 2019, 08:20
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If a and b are integers and |a - b| = 16, what is the minimum possible value of ab?

A . -16
B . -32
C . -48
D . -64
E . -80
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 16 Apr 2019, 09:15
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Given |a-b| = 16
Possible values are (-15,1) (-14,2)......(-8,8)
Here the min value is obtained when the value of a and b are same, but with opposite signs.
a = -8 and b = 8
ab = -64
D is the answer.
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 16 Apr 2019, 16:13
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Hi just want to understand why cant it be -20,4??
once the value is in mod can't it be written as |20-4|=16??
This would give the answer as -80
Am I missing something over hear??
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 16 Apr 2019, 16:32
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if you consider a=20 and b=-4 then |a-b|=24
or if you consider a=-4 and b=-20, even then |a-b|=24
Hence ab can never be equal to -80
devavrat wrote:
Hi just want to understand why cant it be -20,4??
once the value is in mod can't it be written as |20-4|=16??
This would give the answer as -80
Am I missing something over hear??
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 17 Apr 2019, 17:58
btrg wrote:
If a and b are integers and |a - b| = 16, what is the minimum possible value of ab?

A . -16
B . -32
C . -48
D . -64
E . -80


If a = 8 and b = -8 (or, a = -8 and b = 8), we see that |a - b| = 16 and the product ab = -64. Had we choose any other pairs of numbers for a and b, the product would be greater than -64. For example, if a = 7 and b = -9 (or, a = -9 and b = 7), ab = -63. If a = 6 and b = -10 (or a = -10 and b = 6), ab = -60. We see that both -63 and -60 are greater than -64. So -64 is the smallest product for ab.

Answer: D
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 17 Jun 2019, 07:46
nick1816 wrote:
if you consider a=20 and b=-4 then |a-b|=24
or if you consider a=-4 and b=-20, even then |a-b|=24
Hence ab can never be equal to -80
devavrat wrote:
Hi just want to understand why cant it be -20,4??
once the value is in mod can't it be written as |20-4|=16??
This would give the answer as -80
Am I missing something over hear??



But when a=-4 and b=-20, dont we get |a-b|=16 since the negative sign of the equation would cancel the negative sign of b and make it -4+20?
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 17 Jun 2019, 09:27
If a=-4 and b=-20, value of |a-b| will be equal to 16. But product of ab will be equal to 80, not -80.

SarmadIK wrote:
But when a=-4 and b=-20, dont we get |a-b|=16 since the negative sign of the equation would cancel the negative sign of b and make it -4+20?
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Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 12 Jul 2020, 10:03
Why not C ?can any one explain as -48 I less than -64

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If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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New post 12 Jul 2020, 21:02
Deepender wrote:
Why not C ?can any one explain as -48 I less than -64

Posted from my mobile device


Because in a number line the more you move towards left side the smaller the number is.
-64 is on left side of -48. hence -64 is smaller than -48.
So D will be the answer
(how we got D is already explained by others in above comments)
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If a and b are integers and |a - b| = 16, what is the minimum possible   [#permalink] 12 Jul 2020, 21:02

If a and b are integers and |a - b| = 16, what is the minimum possible

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