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X is proportional to Y. If Y is increased by 30%, by approximately

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Math Revolution GMAT Instructor
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X is proportional to Y. If Y is increased by 30%, by approximately [#permalink]

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New post 13 Mar 2018, 00:56
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Question Stats:

53% (01:22) correct 47% (01:34) wrong based on 43 sessions

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[GMAT math practice question]

\(X\) is proportional to \(Y\). If \(Y\) is increased by \(30%\), by approximately what percent is \(X^2\) increased?

\(A. 30%\)
\(B. 40%\)
\(C. 50%\)
\(D. 60%\)
\(E. 70%\)
[Reveal] Spoiler: OA

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X is proportional to Y. If Y is increased by 30%, by approximately [#permalink]

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New post 13 Mar 2018, 11:33
MathRevolution wrote:
[GMAT math practice question]

\(X\) is proportional to \(Y\). If \(Y\) is increased by \(30%\), by approximately what percent is \(X^2\) increased?

\(A. 30%\)
\(B. 40%\)
\(C. 50%\)
\(D. 60%\)
\(E. 70%\)


\(x\) is proportional to \(y\) so let \(x=ky\), where \(k\) is constant of proportionality

so \(x^2=(ky)^2\). When \(y\) is increased by \(30\)%,

\(x=1.3ky\), so \(x^2=1.69(ky)^2\)

Hence there is an increase of \(0.69\) or \(69\)% in the value of \(x^2\). Nearest option is \(70\)%

Option E
Expert Post
Math Revolution GMAT Instructor
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Re: X is proportional to Y. If Y is increased by 30%, by approximately [#permalink]

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New post 15 Mar 2018, 02:24
=>

\(X = kY\) for some \(k\).
Since \((1.3kY)^2 = 1.69k^2Y^2 = 1.69(kY)^2 = 1.69X^2\),
we have \(\frac{(1.69X^2 – X^2)}{X^2} = 0.69\), which is approximately 70%.

Therefore, the answer is E.

Answer: E
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Re: X is proportional to Y. If Y is increased by 30%, by approximately   [#permalink] 15 Mar 2018, 02:24
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