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# If x < y, is x^2 > y^3 ? (1) |x|y < 0 (2) x^3 < y^3

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Director
Joined: 02 Oct 2017
Posts: 691
If x < y, is x^2 > y^3 ? (1) |x|y < 0 (2) x^3 < y^3  [#permalink]

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Updated on: 19 Oct 2018, 03:39
1
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:48) correct 42% (01:39) wrong based on 45 sessions

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If x < y, is x^2 > y^3 ?

(1) |x|y < 0

(2) x^3 < y^3

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Originally posted by push12345 on 19 Oct 2018, 03:36.
Last edited by Bunuel on 19 Oct 2018, 03:39, edited 1 time in total.
Renamed the topic.
Senior Manager
Joined: 19 Oct 2013
Posts: 481
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Re: If x < y, is x^2 > y^3 ? (1) |x|y < 0 (2) x^3 < y^3  [#permalink]

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19 Oct 2018, 03:45
push12345 wrote:
If x < y, is x^2 > y^3 ?

(1) |x|y < 0

(2) x^3 < y^3

We know x < y

Statement 1) tells us that y is negative. x cannot be positive because it will violate the question stem condition.

From question stem let y = -1 and x = - 2

Statement 2) tells us x^3 < y^3

If y = -1 and x = -2 then the answer is yes

If y = 3 and x = 2 then the answe is no.

Insufficient.

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Re: If x < y, is x^2 > y^3 ? (1) |x|y < 0 (2) x^3 < y^3  [#permalink]

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19 Oct 2018, 04:44
push12345 wrote:
If x < y, is x^2 > y^3 ?

(1) |x|y < 0

(2) x^3 < y^3

Question: If x < y, is x^2 > y^3 ?

Since we know that x < y, so for $$x^2$$ to be greater than $$y^3$$ the only possibilities are
1) When both x and y are Negative because $$x^2$$ will always be positive in that case while $$y^3$$ will be be negative
2) when x and y are both in the range 0 to 1 (with constraints $$x^2 > y^3$$

Statement 1: |x|y < 0

i.e. y < 0 hence
SUFFICIENT

Statement 2: x^3 < y^3
Case 1: x = -2 and y = -1 and answer to the question is YES i.e. $$x^2 > y^3$$
Case 2: x = 1/3 and y = 1/2 and answer to the question is NO i.e. $$x^2 < y^3$$
NOT SUFFICIENT

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Re: If x < y, is x^2 > y^3 ? (1) |x|y < 0 (2) x^3 < y^3 &nbs [#permalink] 19 Oct 2018, 04:44
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