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Inequality min and max problem.

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by gmatclubmember » Sat Sep 17, 2011 11:25 pm
suo1987 wrote:If -4<a<4 and -2<b<-1, which of the following could NOT be the value of ab?

A.-3
B.0
C.4
D.6
E.9

Please explain, thank you!
The values of ab would range from (multiply the extreme values of a and b)...(-4)*(-2) to (4)*(-2) so 8 to -8.
So the answer would be E.

Cheers
Ami/-
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by suo1987 » Sun Sep 18, 2011 9:14 am
gmatclubmember wrote:
suo1987 wrote:If -4<a<4 and -2<b<-1, which of the following could NOT be the value of ab?

A.-3
B.0
C.4
D.6
E.9

Please explain, thank you!
The values of ab would range from (multiply the extreme values of a and b)...(-4)*(-2) to (4)*(-2) so 8 to -8.
So the answer would be E.

Cheers
Ami/-
Thanks but why wouldn't -1 be an extreme value of b? Is it because -2 would give the largest range when multiplied?
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by gmatclubmember » Sun Sep 18, 2011 10:42 am
suo1987 wrote:
gmatclubmember wrote:
suo1987 wrote:If -4<a<4 and -2<b<-1, which of the following could NOT be the value of ab?

A.-3
B.0
C.4
D.6
E.9

Please explain, thank you!
The values of ab would range from (multiply the extreme values of a and b)...(-4)*(-2) to (4)*(-2) so 8 to -8.
So the answer would be E.

Cheers
Ami/-
Thanks but why wouldn't -1 be an extreme value of b? Is it because -2 would give the largest range when multiplied?
Yes you are right. Multiply both the extreme values of 'a' with both the extreme values of 'b', and then take the 2 extreme values out of these 4 values.

Cheers
Ami/-
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by sl750 » Sun Sep 18, 2011 11:00 am
Shouldn't it be -4<=b<=-2 and -2<=a<=-1. Otherwise, except for 0 none of them will work
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by suo1987 » Sun Sep 18, 2011 2:12 pm
gmatclubmember wrote:
suo1987 wrote:
gmatclubmember wrote:
suo1987 wrote:If -4<a<4 and -2<b<-1, which of the following could NOT be the value of ab?

A.-3
B.0
C.4
D.6
E.9

Please explain, thank you!
The values of ab would range from (multiply the extreme values of a and b)...(-4)*(-2) to (4)*(-2) so 8 to -8.
So the answer would be E.

Cheers
Ami/-
Thanks but why wouldn't -1 be an extreme value of b? Is it because -2 would give the largest range when multiplied?
Yes you are right. Multiply both the extreme values of 'a' with both the extreme values of 'b', and then take the 2 extreme values out of these 4 values.

Cheers
Ami/-
Thanks again!
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