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If xy>0, is x^3y^4>0?

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Math Revolution GMAT Instructor
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If xy>0, is x^3y^4>0?  [#permalink]

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New post 22 Jan 2018, 01:03
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[GMAT math practice question]

If \(xy>0\), is \(x^3y^4>0?\)

\(1) x>0\)
\(2) y>0\)

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Re: If xy>0, is x^3y^4>0?  [#permalink]

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New post 22 Jan 2018, 10:00
MathRevolution wrote:
[GMAT math practice question]

If \(xy>0\), is \(x^3y^4>0?\)

\(1) x>0\)
\(2) y>0\)


\(x^3y^4>0=>y(xy)^3>0\) as \(xy>0=>(xy)^3>0\). Hence we need to know Is \(y>0\)?

Statement 1: \(x>0\) and we know \(xy>0\) so \(y>0\). Sufficient

Statement 2: directly provides \(y>0\). Sufficient

Option D
Math Revolution GMAT Instructor
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Re: If xy>0, is x^3y^4>0?  [#permalink]

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New post 24 Jan 2018, 01:24
=>

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 question.

Modifying the question:
\(x^3y^4>0\)
\(⇔ x>0\)
since \(y^4>0\) is always true. We can ignore even exponents in inequalities that have \(0\) on one side.
So, the question becomes, ‘is \(x>0\)?’.

Condition 1) is certainly sufficient.

Condition 2):
\(x > 0\) since \(y > 0\) and \(xy > 0\). Thus, condition 2) is also sufficient.

Therefore, D is the answer.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

Answer: D
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Re: If xy>0, is x^3y^4>0?  [#permalink]

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New post 21 May 2019, 03:35
MathRevolution wrote:
[GMAT math practice question]

If \(xy>0\), is \(x^3y^4>0?\)

\(1) x>0\)
\(2) y>0\)


Simplify the question first: it is asking is X>0? The rest of the product term is squared so must be +ve.

Statement 1.

Sufficient, X>0 given


Statement 2.

Since XY>0 and given Y>0 then x has to be >0. Also sufficient.
D Either 1 Or 2 independently sufficient.
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Re: If xy>0, is x^3y^4>0?   [#permalink] 21 May 2019, 03:35
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