Hi,
Let us look at statement 2:
If x >0 and we know that x^3 < x^2, then we can say that 0<x<1
To elaborate, the behavior of x^3 and x^2 across the different values of x are as follows:
==========
When x<0, x^3 < x^2
When x = 0, x^3 = x^2
When 0<x<1, x^3 < x^2
When x = 1, x^3 = x^2
When x > 1, x^3 > x^2
==========
Hence, the answer is D indeed ... Hope this helps.
Thanks.
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One more OA wrong?
Source: Beat The GMAT — Data Sufficiency |
is x^2 < x ?adi_800 wrote:If x > 0, is x^2 < x ?
(1) 0.1 < x < 0.4
(2) x^3 < x^2
[spoiler]OA is D..
I got A[/spoiler]
is x^2-x<0
is x(x-1)<0?
Which means the question is asking is x<0 or x<1
Now,
(1) 0.1 < x < 0.4
clearly x<1. Hence SUFF
(2) x^3 < x^2
x^3-x^2<0
x^2(x-1)<0
x^2 canot be less than 0.
hence x-1<0
x<1
hence SUFF
pick D.
Hope this helps!!
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Or yet another way to see that Statement 2 is sufficient: if x is positive, we can divide on both sides of the inequality by x without needing to worry about reversing the inequality. Doing that, you get x^2 < x, which is what we want to know.adi_800 wrote:If x > 0, is x^2 < x ?
(1) 0.1 < x < 0.4
(2) x^3 < x^2
[spoiler]OA is D..
I got A[/spoiler]
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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Don't know what you did adi, but I get (D).adi_800 wrote:If x > 0, is x^2 < x ?
(1) 0.1 < x < 0.4
(2) x^3 < x^2
[spoiler]OA is D..
I got A[/spoiler]
We are simply checking whether X is a fraction or not by checking this --> x^2 < x
(1) 0.1 < x < 0.4
X is clearly a fraction because its between 0 and 1.
(2) x^3 < x^2
Since 3 x's are smaller than 2 x's, it HAS to be a fraction. Remember fraction squared is smaller than the original fraction. So here fraction cubed is smaller than fraction squared.
So the answer is (D).
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Maybe she did what I did -- forgot that X had to be positive! In which case, X could be negative 1 and the answer would be A! Gotta read the statement carefully. I often screw up on that....
