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![If x is not equal to zero, is 1/x > 1? 1] y/x > y 2]](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If x is not equal to zero, is 1/x > 1? 1] y/x > y 2]"){kind=icon}
01 Jan 2008, 08:54
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If x is not equal to zero, is 1/x > 1?
1] y/x > y
2] x^3 > x^2
Please explain!
1] y/x > y
2] x^3 > x^2
Please explain!
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01 Jan 2008, 09:07
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X is a number not equal to 0. To make 1/x > 1, X must be a number less than 1 but greater than 0. So the question is: is 0 < x < 1?
1. y/x > y
on the surface this may look sufficient, but we have to take negatives into consideration. If Y is a negative number, then X can be any other negative number and Y/X will be positive, thus being larger than Y.
Example:
y=-5
-5/-1 > -5
5 > -5
it works, but plug in -1 for x in the original equation. 1/(-1) > 1 doesn't work
INSUFFICIENT
2. x^3 > x^2
We're trying to find out if X is a fraction between 0 and 1. Any number between 0 and 1 will only get smaller as the raise it to higher powers. The fact that X^3 > X^2 tells us that X is a positive number greater than 1. Plug in a fraction and see for yourself
(1/2)^3 > (1/2)^2
1/8 > 1/4 which isn't true
SUFFICIENT
Statement 2 tells us that 1/x is NOT > 1
Answer B
1. y/x > y
on the surface this may look sufficient, but we have to take negatives into consideration. If Y is a negative number, then X can be any other negative number and Y/X will be positive, thus being larger than Y.
Example:
y=-5
-5/-1 > -5
5 > -5
it works, but plug in -1 for x in the original equation. 1/(-1) > 1 doesn't work
INSUFFICIENT
2. x^3 > x^2
We're trying to find out if X is a fraction between 0 and 1. Any number between 0 and 1 will only get smaller as the raise it to higher powers. The fact that X^3 > X^2 tells us that X is a positive number greater than 1. Plug in a fraction and see for yourself
(1/2)^3 > (1/2)^2
1/8 > 1/4 which isn't true
SUFFICIENT
Statement 2 tells us that 1/x is NOT > 1
Answer B
01 Jan 2008, 14:50
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is 1/x > 1? means that x should be (0,1)
1. y/x > y. means that y may be any number and x e (-∞,0)&(0,1)&(1,+∞). Insufficient.
2. x³ > x² → x*x² > x² → x > 1. So, s e (1,+∞). answer is "No". Sufficient.
is 1/x > 1? means that x should be (0,1)
1. y/x > y. means that y may be any number and x e (-∞,0)&(0,1)&(1,+∞). Insufficient.
2. x³ > x² → x*x² > x² → x > 1. So, s e (1,+∞). answer is "No". Sufficient.
