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# If y is not zero, is y^2 + 2y > y^2+ y?

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Intern
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If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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28 Sep 2013, 07:44
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If y is not zero, is y^2 + 2y > y^2+ y?

(1) y^(odd integer) > y^(even integer)
(2) y^2 + y - 12 = 0
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Sep 2013, 07:55, edited 1 time in total.
Edited the question.

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Re: If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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29 Sep 2013, 13:09
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If y is not zero, is y^2 + 2y > y^2+ y?

Is $$y^2 + 2y > y^2+ y$$? --> is $$y>0$$?

(1) y^(odd integer) > y^(even integer). Since y is not zero, then y^(even integer)>0. So, we can safely divide both parts of the inequality by y^(even integer) --> y^(odd integer - even integer)>1 --> y^(odd integer)>1. y cannot be a negative number (because in this case y^(odd integer)<0), thus y>0. Sufficient.

(2) y^2 + y - 12 = 0 --> $$y=-4<0$$ or $$y=3>0$$. Not sufficient.

Hope it's clear.
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Re: If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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22 Oct 2013, 08:46
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If y is not zero, is y^2 + 2y > y^2+ y?

Is y^2 + 2y > y^2+ y? Can be simplified to y>0?

(1) whether y is positive or negative, y^(even integer) is positive. for y^(odd integer) to be greater than y^(even integer), y can be only positive. So, (1) alone Sufficient.

(2) y^2 + y - 12 = 0 --> y=-4 (-ve) or y=3 (+ve) . Not sufficient.

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If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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17 Jul 2015, 03:02
Hi !
I do not quite understand why statement B is not sufficient- since they tell us at the beginning that Y is not zero therefore Y must be equal to 4 and hence makes this statement sufficient?

Last edited by ady871 on 17 Jul 2015, 03:03, edited 1 time in total.

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Re: If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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17 Jul 2015, 03:22
Hi !
I do not quite understand why statement B is not sufficient- since they tell us at the beginning that Y is not zero therefore Y must be equal to 4 and hence makes this statement sufficient?

The question asks whether y is positive. From (2) we have TWO values of y, one positive, 3, and one negative, -4. So, we cannot answer the question, whether y is positive, which means that this statement is NOT sufficient.
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Re: If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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17 Jul 2015, 03:31
OMG thank you so much! I completely misread the question thinking that it said that Y is not negative.
Thanks for such a quick reply!

Bunuel wrote:
Hi !
I do not quite understand why statement B is not sufficient- since they tell us at the beginning that Y is not zero therefore Y must be equal to 4 and hence makes this statement sufficient?

The question asks whether y is positive. From (2) we have TWO values of y, one positive, 3, and one negative, -4. So, we cannot answer the question, whether y is positive, which means that this statement is NOT sufficient.

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Re: If y is not zero, is y^2 + 2y > y^2+ y? [#permalink]

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14 Oct 2017, 05:55
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Re: If y is not zero, is y^2 + 2y > y^2+ y?   [#permalink] 14 Oct 2017, 05:55
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