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If x = 63% of y, then y^2 is approximately what percent of x^2 ?

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Bunuel
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If x = 63% of y, then y^2 is approximately what percent of x^2 ? [#permalink] New post   10 Jan 2021, 06:42
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If x = 63% of y, then y^2 is approximately what percent of x^2 ?

A. 125%
B. 200%
C. 250%
D. 350%
E. 363%
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C
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Re: If x = 63% of y, then y^2 is approximately what percent of x^2 ? [#permalink] New post   10 Jan 2021, 06:59
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Bunuel wrote:
If x = 63% of y, then y^2 is approximately what percent of x^2 ?

A. 125%
B. 200%
C. 250%
D. 350%
E. 363%


\(x = \frac{63}{100}y\)

i.e. \(y = \frac{100}{63}x\)

i.e. \(y^2 = \frac{10000}{63^2}x^2\)

Let, \(y^2\) is k% of \(x^2\)

i.e. \(y^2 = \frac{k}{100}x^2\)

I.E. \(\frac{k}{100} = \frac{10000}{63^2}\)

i.e. \(k = \frac{1000000}{63^2}\)

i.e. \(k ≈ 252%\)

Answer: Option C
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Re: If x = 63% of y, then y^2 is approximately what percent of x^2 ? [#permalink] New post   10 Jan 2021, 08:33
x= (63/ 100) x y
y= (100/ 63) x x
y^2= (100^2/63^2) x x^2

-> 100^2= 10000 63^2= 3969 almost 4000

10000/4000= 5/2= 2,5 x 100= 250%
answer C
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Re: If x = 63% of y, then y^2 is approximately what percent of x^2 ? [#permalink] New post   10 Jan 2021, 11:06
If x = 63% of y, then y^2 is approximately what percent of x^2 ?

A. 125%
B. 200%
C. 250%
D. 350%
E. 363%
\(x = 0.63 * y\)
\(y = \frac{x}{0.63}\)
\(y= \frac{100}{63} * x\)
\(y ≈ 1.6 * x\)
\(y ≈ 1.6*1.6*x^2\)
\(y ≈ 2.56 * x^2\)

Since options are widely distributed, we can choose C.

Answer C.
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Re: If x = 63% of y, then y^2 is approximately what percent of x^2 ? [#permalink] New post   12 Dec 2023, 10:35
x=63/100 of y

y=100/63 of x

y^2= 100x100/63x63x100 x^2
y^2= 10000/3969x100
y^2=251.953%
approximately 250%

Thus, correct answer is C.

Am I using the right approach?
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Re: If x = 63% of y, then y^2 is approximately what percent of x^2 ? [#permalink]
12 Dec 2023, 10:35
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