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

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Manager
Joined: 31 Oct 2018
Posts: 76
Location: India
If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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16 Apr 2019, 08:20
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35% (medium)

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65% (01:27) correct 35% (01:49) wrong based on 284 sessions

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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
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1143
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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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
Manager
Joined: 19 Feb 2019
Posts: 119
Location: India
Concentration: Marketing, Statistics
GMAT 1: 650 Q46 V34
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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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16 Apr 2019, 16:13
1
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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Joined: 19 Oct 2018
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Location: India
Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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16 Apr 2019, 16:32
1
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??
Target Test Prep Representative
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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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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.

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Joined: 16 Jul 2017
Posts: 1
Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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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?
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 2062
Location: India
Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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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.

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?
Intern
Joined: 20 Mar 2017
Posts: 14
Re: If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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

Posted from my mobile device
Intern
Joined: 20 Jun 2019
Posts: 2
If a and b are integers and |a - b| = 16, what is the minimum possible  [#permalink]

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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)
If a and b are integers and |a - b| = 16, what is the minimum possible   [#permalink] 12 Jul 2020, 21:02