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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] New post 18 Jul 2003, 11:41
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1. if a < -1 , is b between 0 and 1?
a. -b < -a
b. -1 < ab < 0
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 [#permalink] New post 19 Jul 2003, 05:59
why not D .. the question is whether the value of b lies in 0 and 1 ?
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 [#permalink] New post 19 Jul 2003, 08:45
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.
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 [#permalink] New post 19 Jul 2003, 19:10
Any experts care to explain how to solve the (2) condition?
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 [#permalink] New post 19 Jul 2003, 19:37
kpadma wrote:
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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 [#permalink] New post 26 Jan 2004, 08:43
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.
  [#permalink] 26 Jan 2004, 08:43
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if a < -1 , is b between 0 and 1? a. -b < -a b. -1

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