is x>0 (GMAT Prep)

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Source: — Data Sufficiency |

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by theCEO » Mon Jul 02, 2012 9:35 pm
ax = -b
1)a + b > 0
a + (-ax) > 0
a - ax > 0
a(1-x) > 0
if a is negative (1-x) is negative - > x positive
if a is positive (1-x) is positive -> x is positive or negative
statement is not valid by itself

2)a - b > 0
a + ax > 0
a (1+x) > 0
if a is negative, (1+x) is negative -> x is negative
if a is positive, (1+x) is positive -> x is positive or negative
statement is not valid by itself


combination: add eq1 and eq2
2a > 0 -> a > 0
Positive x (x)+ b = 0
Positive x (x) = - b
If x is positive -> b is negative
If x is negative -> b is positive
Combination doesn't work either.
Last edited by theCEO on Mon Jul 02, 2012 9:47 pm, edited 1 time in total.

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by Anurag@Gurome » Mon Jul 02, 2012 9:46 pm
alex.gellatly wrote:If ax + b = 0, is x>0

1. a+b >0
2. a-b > 0
(ax + b) = 0 ---> x = -b/a
Therefore, x will be positive only if a and b are of opposite signs.

Now, consider the following cases,
  • a = 2, b = 1 --> x = -b/a = -2 < 0
    a = 2, b = -1 --> x = -b/a = 2 > 0
Both of the above cases satisfy both the statements but in the first case x < 0, and in the second x > 0

Hence, both statements together is also not sufficient.

The correct answer is E.
Anurag Mairal, Ph.D., MBA
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