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if r is halved V is multiplied by

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by Brent@GMATPrepNow » Tue Mar 04, 2014 12:26 pm
BlueDragon2010 wrote:In the formula V = 1/(2r)³, if r is halved then V is multiplied by

A) 64
B) 8
C) 1
D) 1/8
E) 1/64
A quick approach here is to plug in a "nice" number.
Let's plug in r = 1. We get V = 1/[(2)(1)]³ = 1/8

Now let's see what happens when we HALVE r. In other words, we'll plug in r = 1/2.
We get V = 1/[(2)(1/2)]³ = 1

So, when r = 1, V = 1/8, and when r = 1/2, V = 1.

So, when we halve r, V is multiplied by 8

Answer = B

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by Patrick_GMATFix » Tue Mar 04, 2014 12:32 pm
I might plug in values (r=1 --> 1/2 for instance), or just replace r with r/2 and compare the original V to the new V. The answer is B. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by [email protected] » Tue Mar 04, 2014 2:25 pm
Hi BlueDragon2010,

This question is perfect for TESTing Values, as Brent's solution showcases.

If you'd rather do algebra, here's how you could solve this problem:

V = 1/(2r)^3

V = 1/8r^3

This is the "starting value"

The question asks us to HALVE the value of r, so we'd then start with this....

V = 1/(r)^3

V = 1/r^3

Compare the denominators of both fractions and you'll see that the denominator went from 8r^3 to r^3, meaning that the denominator was divided by 8. When you divide the denominator of a fraction by 8, the OVERALL fraction becomes 8 times BIGGER.

Final Answer: B

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