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EBITDA
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A sphere with radius x shrinks by a% in volume. What is the new... 11 Aug 2016, 11:26
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Difficulty:

55% (hard)

Question Stats:

69% (02:34) correct 31% (01:55) wrong based on 13 sessions

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A sphere with radius x shrinks by a% in volume. What is the new radius of the resulting sphere, in terms of x and a?

A) x^3 * \(\sqrt{(a/100)}\)
B) x^3 * \(\sqrt{(1 - (a/100))}\)
C) 4/3 * π * x^3 * \(\sqrt{(1 - (a/100))}\)
D) x^3 * \(\sqrt{(100 / (100 - a))}\)
E) 4/3 * π * x^3 * \(\sqrt{(100 / (100 - a))}\)

Please develop in detail your answer so that we can all follow it.



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BrentGMATPrepNow
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A sphere with radius x shrinks by a% in volume. What is the new... 11 Aug 2016, 11:33
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EBITDA
A sphere with radius x shrinks by a% in volume. What is the new radius of the resulting sphere, in terms of x and a?

A) x^3 * \(\sqrt{(a/100)}\)
B) x^3 * \(\sqrt{(1 - (a/100))}\)
C) 4/3 * π * x^3 * \(\sqrt{(1 - (a/100))}\)
D) x^3 * \(\sqrt{(100 / (100 - a))}\)
E) 4/3 * π * x^3 * \(\sqrt{(100 / (100 - a))}\)

Please develop in detail your answer so that we can all follow it.
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Hi EBITDA,

What's the source of this question? I ask because the GMAT does not require test-takers to know the formula for the volume of a sphere. In a question like this, you would be provided with that formula: Volume = (4/3)πr³
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A sphere with radius x shrinks by a% in volume. What is the new... 11 Aug 2016, 11:40
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Initial radius of the sphere is x
Volume =4/3* π* x^3

Volume is shrinked by a%
=> new volume = (100-a)/100*(4/3* π* x^3)

let the new radius be y
new volume =4/3* π* y^3
=>4/3* π* y^3= (100-a)/100*(4/3* π* x^3)

=> y^3= ((100-a)/100)* x^3
=>y^3= (1-a/100)* x^3

Is'nt this the solution.
Can somebody verify this.
thanks in advance.
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A sphere with radius x shrinks by a% in volume. What is the new... 13 Aug 2016, 10:40
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ShravyaAlladi
Initial radius of the sphere is x
Volume =4/3* π* x^3

Volume is shrinked by a%
=> new volume = (100-a)/100*(4/3* π* x^3)

let the new radius be y
new volume =4/3* π* y^3
=>4/3* π* y^3= (100-a)/100*(4/3* π* x^3)

=> y^3= ((100-a)/100)* x^3
=>y^3= (1-a/100)* x^3

Is'nt this the solution.
Can somebody verify this.
thanks in advance.
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I also followed the same approach.

Since, the question is asking for the new radius, we can say

y = (1-a/100)^1/3 * x

But none of the options given has this answer.

EBITDA, can you please confirm if the answers you mentioned are actually correct?

Please let me know if I am missing anything.
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A sphere with radius x shrinks by a% in volume. What is the new... 29 May 2017, 03:36
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Hey!

I'll try to explain it..


Volume of sphere with radius x = \(Vx = \frac{4}{3}*π*x^3\)
Volume of sphere with radius y = \(Vx = \frac{4}{3}*π*y^3\)

Now shrink the Vx by a%:

\(\frac{100-a}{100}*Vx = \frac{100-a}{100}*\frac{4}{3}*π*x^3\)

This new volume has to be the same than the Vy:

\(\frac{100-a}{100}*\frac{4}{3}*π*x^3 = \frac{4}{3}*π*y^3\)

\(\frac{100-a}{100}*x^3 = y^3 = (1-\frac{a}{100})*x^3\)

Then..

\(y = x*\sqrt[3]{1-\frac{a}{100}}\)

For me it's B

PD: I think the answers have a typo, where it puts \(x^3*\sqrt{...}\) means \(x*\sqrt[3]{...}\)
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A sphere with radius x shrinks by a% in volume. What is the new... 31 May 2017, 17:06
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guillemgc


PD: I think the answers have a typo, where it puts \(x^3*\sqrt{...}\) means \(x*\sqrt[3]{...}\)
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I hope you are right, because this question is driving me crazy.

Nice analysis, BTW!



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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