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Algebra

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by light_speed » Wed Apr 09, 2008 3:50 pm
If x and y are positive, is x^3> y?
(1)sqrt x> y
(2) x > y

The answer is showing as E, none, . I selected D

My logic:-
For the first option, if you square root a number, it becomes smaller, hence if the square root of x is larger than y, does that not mean x >y?

If x>y, and is positive, should not x^3 also be the same?.
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Source: — Data Sufficiency |

Re: Algebra

by Stuart@KaplanGMAT » Wed Apr 09, 2008 4:05 pm
light_speed wrote:If x and y are positive, is x^3> y?
(1)sqrt x> y
(2) x > y

The answer is showing as E, none, . I selected D

My logic:-
For the first option, if you square root a number, it becomes smaller, hence if the square root of x is larger than y, does that not mean x >y?

If x>y, and is positive, should not x^3 also be the same?.
The answer is (e) because you forgot about positive fractions, which get smaller as you raise them to a higher exponent.

For example, (1/2)^2 = 1/4, which is less than 1/2.
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by cjiang16 » Wed Apr 09, 2008 10:40 pm
The answer is E. Say x=-2, y=-3
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by Stuart@KaplanGMAT » Thu Apr 10, 2008 11:00 am
cjiang16 wrote:The answer is E. Say x=-2, y=-3
The stem says "if x and y are positive", so those numbers don't count!
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Re: Algebra

by freedsl » Thu Apr 10, 2008 7:56 pm
Stuart Kovinsky wrote:
light_speed wrote:If x and y are positive, is x^3> y?
(1)sqrt x> y
(2) x > y

The answer is showing as E, none, . I selected D

My logic:-
For the first option, if you square root a number, it becomes smaller, hence if the square root of x is larger than y, does that not mean x >y?

If x>y, and is positive, should not x^3 also be the same?.
The answer is (e) because you forgot about positive fractions, which get smaller as you raise them to a higher exponent.

For example, (1/2)^2 = 1/4, which is less than 1/2.
Stuart , can you elaborate on case (1). I see your point about positive fractions related to x>y but not for x^2>y. if x^2>y, doesn't that mean that x is larger than 1 and its not a fraction between 0 and 1. thanks
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