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# If x is less than y, is x^2 less than y^2?

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If x is less than y, is x^2 less than y^2? [#permalink]  11 Aug 2007, 03:34
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If x is less than y, is x^2 less than y^2?
(1) y > 0
(2) x > 0

Last edited by misterJJ2u on 12 Aug 2007, 16:58, edited 1 time in total.
Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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If x is less than y, is x^2 less than y^2? [#permalink]  11 Aug 2007, 10:38
could you repost the question..this time disble HTML in the post!
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Re: DS_is x^2 less than y^2? [#permalink]  12 Aug 2007, 17:39
misterJJ2u wrote:
(edit: disabled HTML)

---------------------------------------

If x is less than y, is x^2 less than y^2?
(1) y > 0
(2) x > 0

this is B.
1. y is +ve, but lxl>y. nsf.
2. if both are +ve and y>x, x^2<y^2. suff.

B
Director
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Given: X < Y
X ² - Y² < 0
This can be expressed as (X + Y) (X – Y) <0> 0
This scenario, Y is a positive number and X is positive or negative number. This condition proves to be invalid if X = -1 and Y = 1. This is insufficient.

Case 2: X > 0

This condition imposes a pre-condition of both X and Y are positive numbers and X is less than Y. For example: X = 2 Y = 3 ect. This is sufficient to prove that both (X + Y) (X – Y) < 0

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