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# if a < -1 , is b between 0 and 1? a. -b < -a b. -1

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Director
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if a < -1 , is b between 0 and 1? a. -b < -a b. -1 [#permalink]

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18 Jul 2003, 12:41
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1. if a < -1 , is b between 0 and 1?
a. -b < -a
b. -1 < ab < 0
Manager
Joined: 25 Jun 2003
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19 Jul 2003, 06:59
why not D .. the question is whether the value of b lies in 0 and 1 ?
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Brainless

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19 Jul 2003, 09:45
Brainless wrote:
why not D .. the question is whether the value of b lies in 0 and 1 ?

from 1..
-b < -a
=> b > a
=> b > -1. this does not necessarily mean that b is between 0 and 1.
Director
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19 Jul 2003, 20:10
Any experts care to explain how to solve the (2) condition?
GMAT Instructor
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19 Jul 2003, 20:37
Any experts care to explain how to solve the (2) condition?

we are given -1 < ab < 0.

Since a < -1, we know it is always negative. Lets divide every term by a, remembering to flip the inequality because we are dividing by a negative.

We get:

-1/a > b > 0.

Since a is always negative, -1/a is always postive so we can say.

1/|a| > b > 0.

Since a < -1, the magnitute of a is always greater than 1 and hence, the fraction 1/|a| is always less than 1 but positive. Hence 1 > b > 0.
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Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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26 Jan 2004, 09:43
Condition a)
let us say a = -1 then -a = 1
if -b < 1 then b could be 0 or 0.5 or 2 since
0 < 1, -0.5 < 1 and -2 < 1. We cannot say anything from this condition.

Condition b)
0 < ab < 1
We know that a is -ve. So b has to be positive. Also b cannot be 0.
if a = -1 ( the boundary condition ) then if you let b = 1 then
ab = -1 and does not satisfy the condition b) so b has to lie between 0 and 1.
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