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Is x² - y > 1/y² where y is non-zero?

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Intern
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Joined: 28 May 2018
Posts: 41
Location: India
Schools: Tuck '21, ISB '20, NTU '20
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
Is x² - y > 1/y² where y is non-zero?  [#permalink]

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New post 19 Oct 2018, 01:49
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

45% (02:14) correct 55% (02:13) wrong based on 20 sessions

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Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

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Please +1 KUDO if my post helps. Thank you.

Intern
Intern
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Joined: 28 May 2018
Posts: 41
Location: India
Schools: Tuck '21, ISB '20, NTU '20
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

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New post 19 Oct 2018, 02:10
This is the solution that I found. I do not find this explanation satisfactory.

Can any of the experts please explain the solution better? Thanks in advance :)

Let's start by simplifying the original by multiplying both sides by y² (we can safely do so because we know that y² is positive):
Is \(x^2y^3\) - \(y^3\) > 1?
(1) x < y
If x and y are big positive numbers, \(y^3\) will dominate x²y² and the left side will be negative; if x and y are big negative numbers, x²y² and (-\(y^3\)) will both be positive and the left side will be a big positive number: insufficient.
(2) x² < y²
Tells us that |x| < |y|, but nothing about the signs of x and y. If we pick really big values with different signs we can generate both "yes" and "no" answers.
Together: combining doesn't help us at all, since we have the same generalizations from both: choose E.
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GMAT Club Bot
Re: Is x² - y > 1/y² where y is non-zero? &nbs [#permalink] 19 Oct 2018, 02:10
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Is x² - y > 1/y² where y is non-zero?

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