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Is x^2 + xy > 5xy – 4y^2?

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Is x^2 + xy > 5xy – 4y^2? [#permalink]

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New post 17 Nov 2017, 00:13
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[GMAT math practice question]

Is \(x^2 + xy > 5xy – 4y^2\)?

1) \(x > 2y\)
2) \(x > y\)
[Reveal] Spoiler: OA

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Re: Is x^2 + xy > 5xy – 4y^2? [#permalink]

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New post 17 Nov 2017, 01:19
MathRevolution wrote:
[GMAT math practice question]

Is \(x^2 + xy > 5xy – 4y^2\)?

1) \(x > 2y\)
2) \(x > y\)



Get the terms to one side to simplify..
\(x^2+xy>5xy-4y^2........x^2-4xy+4y^2>0......(x-2y)^2>0\)
The left side will always be non negative as it is to power of 2..
So ans will be YES other than when x=2y

Let's check the statements..

1) x>2y
So clearly x is NOT EQUAL to 2y... Yes
Sufficient

2) x>y...
If x =2y and is NO
Otherwise YES
Insufficient

A
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Re: Is x^2 + xy > 5xy – 4y^2? [#permalink]

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New post 19 Nov 2017, 17:22
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the numbers of variables and equations.

Modifying the original condition and question:
\(x^2 + xy > 5xy – 4y^2\)
⇔ \(x^2 - 4xy + 4y^2 > 0\)
⇔\((x – 2y)^2 > 0\)
⇔ \(x ≠ 2y\)
The question, ‘Is \(x^2 + xy > 5xy – 4y^2\) ?’, is equivalent to asking if \(x ≠ 2y\).

Condition 1)
This is sufficient because \(x > 2y\) implies that \(x ≠ 2y\).

Condition 2)
If x=3 and y=1, then \((x-2y)^2=1>0\), and the answer is ‘yes’.
If x=2 and y=1, then \((x-2y)^2=0\), and the answer is ‘no’.
This is NOT sufficient.

Therefore, the answer is A.

Answer: A
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Re: Is x^2 + xy > 5xy – 4y^2?   [#permalink] 19 Nov 2017, 17:22
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