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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # In the formula V = 1/(2r)^3, if r is halved, then V is multi

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Senior Manager  Joined: 10 Mar 2008
Posts: 302
In the formula V = 1/(2r)^3, if r is halved, then V is multi  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:05) correct 28% (01:15) wrong based on 471 sessions

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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

Originally posted by vksunder on 15 Jul 2008, 12:39.
Last edited by Bunuel on 21 Feb 2014, 05:10, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Math Expert V
Joined: 02 Sep 2009
Posts: 55266
Re: In the formula V= 1/(2r)^3, if r is halved, then V is  [#permalink]

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2
6
benjamin09 wrote:
Can someone solve this question with an explanation?

Thanks

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

Given: $$V = \frac{1}{(2r)^3}=\frac{1}{8r^3}$$

Now, halved r is r/2, substitute r/2 instead of r: $$V' = \frac{1}{(2*\frac{r}{2})^3}=\frac{1}{r^3}$$.

$$V =\frac{1}{8r^3}$$ should be multiplied by 8 to get $$V'=\frac{1}{r^3}$$.

Answer: B.

Or:
When r=2, then $$V = \frac{1}{(2r)^3}=\frac{1}{64}$$.
When r=1, then $$V' = \frac{1}{(2r)^3}=\frac{1}{8}$$.

1/64 should be multiplied by 8 to get 1/8.

Answer: B.

Similar question to practice: if-the-function-q-is-defined-by-the-formula-q-5w-4x-z-131051.html

Hope it helps.
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SVP  Joined: 30 Apr 2008
Posts: 1801
Location: Oklahoma City
Schools: Hard Knocks
Re: PS: formula V= 1/(2r)^3  [#permalink]

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B - about had that backwards  Make r = 1/2, V = 1

Make r = 1, v = 1/8
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Senior Manager  Joined: 07 Jan 2008 Posts: 250 Re: PS: formula V= 1/(2r)^3 [#permalink] ### Show Tags I always mess up these kinds... Say r=2 => V1 = 1/64 when r=1; V2 = 1/8 V2 = 8*V1. B? SVP  Joined: 30 Apr 2008 Posts: 1801 Location: Oklahoma City Schools: Hard Knocks Re: PS: formula V= 1/(2r)^3 [#permalink] ### Show Tags I totally agree with you. I mess them up to and about did this one. I saw that if I make 2r = 1, then r=1/2 so to the power of 3 doesn't matter, it's still 1/1. Then I did r =1 (double it) so then V = 1/8. So I was thinking oh, go from 1 to 1/8 multiply by 1/8...but I had worked the problem backwards. There are tricks the authors throw at us, and then there are tricks we bring to the test ourselves. We have to eliminate our own tricks. Easier said than done! mbawaters wrote: I always mess up these kinds... Say r=2 => V1 = 1/64 when r=1; V2 = 1/8 V2 = 8*V1. B? _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Senior Manager  Joined: 10 Mar 2008
Posts: 302
Re: PS: formula V= 1/(2r)^3  [#permalink]

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So isnt the qtn essentially testing us on: if r is halved then what should V be multiplied by to retain the intial formula???
Senior Manager  Joined: 07 Jan 2008
Posts: 250
Re: PS: formula V= 1/(2r)^3  [#permalink]

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vksunder wrote:
So isnt the qtn essentially testing us on: if r is halved then what should V be multiplied by to retain the intial formula???

I think its asking us to reflect the changes in the value of V if r is halved!
Senior Manager  Joined: 09 Oct 2007
Posts: 438
Re: PS: formula V= 1/(2r)^3  [#permalink]

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vksunder wrote:
So isnt the qtn essentially testing us on: if r is halved then what should V be multiplied by to retain the intial formula???

Not really, it's asking what happens to V when r is halved. In this type of problems, just pick an easy value for r and solve both equations.
Intern  Joined: 29 Jan 2014
Posts: 17
GMAT 1: 510 Q36 V26 GMAT 2: 550 Q38 V28 Re: In the formula V= 1/(2r)^3, if r is halved, then V is  [#permalink]

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Can someone solve this question with an explanation?

Thanks
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GMAT 1: 510 Q36 V26 GMAT 2: 550 Q38 V28 Re: In the formula V = 1/(2r)^3, if r is halved, then V is multi  [#permalink]

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Thanks a lot Bunuel!
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the formula V = 1/(2r)^3, if r is halved, then V is multi  [#permalink]

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Hi All,

This question is perfect for TESTing Values.

IF... R=2
V = (1/(2x2)^3 = 1/64

Halving R gives us R=1...
V = (1/2x1)^3 = 1/8

1/8 = 8/64...
so going from 1/64 to 8/64 means that V increased 8 times.

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Re: In the formula V = 1/(2r)^3, if r is halved, then V is multi  [#permalink]

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Bunuel wrote:
benjamin09 wrote:
Can someone solve this question with an explanation?

Thanks

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

Given: $$V = \frac{1}{(2r)^3}=\frac{1}{8r^3}$$

Now, halved r is r/2, substitute r/2 instead of r: $$V' = \frac{1}{(2*\frac{r}{2})^3}=\frac{1}{r^3}$$.

$$V =\frac{1}{8r^3}$$ should be multiplied by 8 to get $$V'=\frac{1}{r^3}$$.

Answer: B.

Or:
When r=2, then $$V = \frac{1}{(2r)^3}=\frac{1}{64}$$.
When r=1, then $$V' = \frac{1}{(2r)^3}=\frac{1}{8}$$.

1/64 should be multiplied by 8 to get 1/8.

Answer: B.

Similar question to practice: http://gmatclub.com/forum/if-the-functi ... 31051.html

Hope it helps.

why answer is B amd not D ? Target Test Prep Representative G
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Re: In the formula V = 1/(2r)^3, if r is halved, then V is multi  [#permalink]

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vksunder 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

Since (2r)^3 = 8r^3, we can rewrite the formula as V = 1/(8r^3).

Let’s substitute r/2 instead of r in the first equation: V = 1/(2(r/2))^3 = 1/r^3 = 8*1/(8r^3).

As we can see, when we halve r, V gets multiplied by 8.

Alternate Solution:

Let’s let the original value of r = 2. Substituting 2 for r into the original equation yields:

Original V = 1/[(2)(2)]^3,

Original V = 1/(4)^3

Original V = 1/64

Now we halve r, so it is now equal to 1. Substituting 1 for r gives us:

New V = 1/[(2)(1)]^3

New V = 1/ 8

We see that the original value of V (1/64), when multiplied by 8, gives us the new value of V:

(1/64) x 8 = 8/64 = 1/8

Answer: B
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