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Is −x < (1/x)?

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by sanju09 » Fri Mar 02, 2012 2:32 am
Is −x < (1/x)?
(1) x < −1.
(2) |x| > 0.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Mar 02, 2012 5:00 am
sanju09 wrote:Is −x < (1/x)?
(1) x < −1.
(2) |x| > 0.
(1) x < -1 implies x will always be negative.
So, -x will always be positive and 1/x will always be negative. Hence, -x > 1/x always; SUFFICIENT.

(2) |x| > 0
If x = -2, then -x = 2, and 1/x = -1/2. Here −x > (1/x).
If x = 2, then -x = -2, and 1/x = 1/2. Here −x < (1/x).
No definite answer; NOT sufficient.

The correct answer is A.
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by krusta80 » Fri Mar 02, 2012 5:50 am
sanju09 wrote:Is −x < (1/x)?
(1) x < −1.
(2) |x| > 0.
We can rewrite this as two possible equations:

x^2 > -1, for x > 0 ALWAYS TRUE
x^2 < -1, for x < 0 NEVER TRUE

In other words, we have SUFFICIENCY as long as x is on one side of the number line.

(1) x < -1

SUFFICIENT -> -x is not less than 1/x ever

(2) |x| > 0

INSUFFICIENT -> answer depends on the sign of x, which is not restricted here

A
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