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M31-46

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M31-46 [#permalink]

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New post 20 Jun 2015, 10:46
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A
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Question Stats:

50% (01:32) correct 50% (01:36) wrong based on 24 sessions

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Re M31-46 [#permalink]

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Official Solution:


Is \(x > y\)?

(1) \(a*x^4 + a*|y| < 0\).

Factor out \(a\): \(a(x^4 + |y|) < 0\). Since \(x^4 + |y| = nonnegative + nonnegative = nonnegative\), then for \(a*nonnegative\) to be negative, a must be negative. We know nothing about \(x\) and \(y\). Not sufficient.

(2) \(a*x^3 > a*y^3\).

If \(a\) is positive, then when reducing by it, we'll get \(x^3 > y^3\), or which is the same \(x > y\) BUT if \(a\) is negative, then when reducing by negative value and flipping the sign, we'd get \(x^3 < y^3\), or which is the same \(x < y\). Not sufficient.

(1)+(2) Since from (1) \(a < 0\), then from (2) \(x < y\). Sufficient.


Answer: C
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Re M31-46 [#permalink]

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New post 24 Aug 2016, 04:15
I think this is a high-quality question and I agree with explanation.
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M31-46 [#permalink]

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New post 10 Oct 2016, 17:19
Bunuel : How do we know x<y when x^3 < y^3 ------ this is only true if X and Y are not fractions
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Re: M31-46 [#permalink]

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utkarsh240884 wrote:
Bunuel : How do we know x<y when x^3 < y^3 ------ this is only true if X and Y are not fractions


You could simply test your theory with fractions to test whether it's true.

We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).

Check the links below:
Inequalities Made Easy!

Solving Quadratic Inequalities - Graphic Approach
Inequality tips
Wavy Line Method Application - Complex Algebraic Inequalities

DS Inequalities Problems
PS Inequalities Problems

700+ Inequalities problems

inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html

Hope it helps.
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Re: M31-46 [#permalink]

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New post 16 Nov 2017, 04:49
For statement 1 to be true, cant all three be fractions ?

[quote="Bunuel"]

You could simply test your theory with fractions to test whether it's true.

We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).
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Re: M31-46 [#permalink]

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New post 16 Nov 2017, 04:54
HariharanIyeer0 wrote:
For statement 1 to be true, cant all three be fractions ?



From (1) all we can deduce is that a is negative (and that not both from x and y are 0). Other than that, the variables could be integers, fractions, or irrational numbers, we don't know that.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M31-46   [#permalink] 16 Nov 2017, 04:54
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