Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 15:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The variables a and b are non-zero integers. If a = 2b^3/c, what happe

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56304
The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 00:51
2
2
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:39) correct 31% (01:43) wrong based on 146 sessions

### HideShow timer Statistics

The variables a and b are non-zero integers. If a = 2b^3/c, what happens to c when a is halved and b is doubled?

A. c is not changed.
B. c is halved.
C. c is doubled.
D. c is multiplied by 4.
E. c is multiplied by 16.

Kudos for a correct solution.

_________________
Manager
Joined: 26 Dec 2011
Posts: 115
Schools: HBS '18, IIMA
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 02:31
2
1
Bunuel wrote:
The variables a and b are non-zero integers. If a = 2b^3/c, what happens to c when a is halved and b is doubled?

A. c is not changed.
B. c is halved.
C. c is doubled.
D. c is multiplied by 4.
E. c is multiplied by 16.

Kudos for a correct solution.

Solution -

Given that a = 2*b^3/c --> c = 2*b^3/a

What is the value of c when a->a/2 and b->2b.

c = 2*b^3/a = 2*(2b)^3/(a/2) = 2*2*8*b^3/a = 16*(2*b^3/a)

The value of c is 16 times the original value. ANS E.
_________________
Thanks,
CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 03:47
Bunuel wrote:
The variables a and b are non-zero integers. If a = 2b^3/c, what happens to c when a is halved and b is doubled?

A. c is not changed.
B. c is halved.
C. c is doubled.
D. c is multiplied by 4.
E. c is multiplied by 16.

Kudos for a correct solution.

Assume a=2, b =1 000----> c = 2(1)/2 =1

Final value of c = with b =2 and a=1 ---> c = 2(2)^3/1 ---> c = 16. Thus C is multiplied by 16. E is the correct answer.
Intern
Joined: 19 May 2015
Posts: 7
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 04:06
1
if a is divided by 2, the whole equation is divided by two - a/2=(2b^3/c)/2 => a/2=2b^3/2c - it means that c has to be halved
if b is doubled - b^3 is multiplied by 8, which means that c also has to be multiplied by 8 to keep the equation.
hence, C is halved and than multiplied by 8, so correct answer is D - multiplied by 4.
CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 04:15
Tornikea wrote:
if a is divided by 2, the whole equation is divided by two - a/2=(2b^3/c)/2 => a/2=2b^3/2c - it means that c has to be halved
if b is doubled - b^3 is multiplied by 8, which means that c also has to be multiplied by 8 to keep the equation.
hence, C is halved and than multiplied by 8, so correct answer is D - multiplied by 4.

The text in red above is not correct. When you half 'a' , c gets multiplied by 2.

c=(2b^3)/(a/2) = 2* (2b^3)/a

Thus, the final effect will be to multiply c by 2 and then by 8 in effect multiplying by 16.
Senior Manager
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 05:12
1
$$a = \frac{2b^3}{c}$$, so $$c = \frac{2b^3}{a}$$.

when $$a$$ is halved and $$b$$ is doubled, c = $$\frac{2*2(2b)^3}{a}$$ = $$\frac{32b^3}{a}$$.

so, $$c$$ is multiplied by 16 when $$a$$ is halved and $$b$$ is doubled. Ans (E).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Intern
Joined: 21 Jul 2015
Posts: 2
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 08:12
1
When a = 2 and b = 2 ; C = 8
a*.5 = 1
b *2 = 4

When a = 1 and b = 4 ; C = 128

8x = 128
x = 16
Intern
Joined: 08 Jun 2015
Posts: 3
GPA: 3.9
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 10:48
1
rearrange equation so that you have c=(2b^3)/a

a=2 b=1
c=1

a=1 b=2
c=16

_________________
GMATPrep1=>720
GMATPrep2=>760
Intern
Joined: 08 Jul 2012
Posts: 46
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

24 Jul 2015, 10:56
1
Bunuel wrote:
The variables a and b are non-zero integers. If a = 2b^3/c, what happens to c when a is halved and b is doubled?

A. c is not changed.
B. c is halved.
C. c is doubled.
D. c is multiplied by 4.
E. c is multiplied by 16.

Kudos for a correct solution.

a=2b^3/c

c=2b^3/a

when a is halved and b is doubled

c=2(2b)^3/(a/2)
c=16*2b^3/a

Ans. E c is multiplied by 16.
_________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison
Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

26 Jul 2015, 12:20
Bunuel wrote:
The variables a and b are non-zero integers. If a = 2b^3/c, what happens to c when a is halved and b is doubled?

A. c is not changed.
B. c is halved.
C. c is doubled.
D. c is multiplied by 4.
E. c is multiplied by 16.

Kudos for a correct solution.

800score Official Solution:

The easiest way to solve this problem is to plug in numbers for the variables and then backsolve for c. Use even numbers, because even numbers can be halved without leaving fractions.

Let b = 2 and c = 4. Solve the equation:
a = (2(2³))/4 = 16/4 = 4.
So, a = 4 when b = 2 and c = 4.

Now halve a and double b: a = 2, b = 4. Plug these values into the equation and see what happens to c:
2 = ((2(4³))/c
2 = (2(64))/c
2 = 128/c
2c = 128
c = 64.

Comparing this to the original value of c, which was 4, we see that the new value for c is 16 times the original value.

Another way to attack this problem is to solve for c to arrive at the same answer.

The correct answer is choice (E).
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 11720
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe  [#permalink]

### Show Tags

16 Jul 2018, 07:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The variables a and b are non-zero integers. If a = 2b^3/c, what happe   [#permalink] 16 Jul 2018, 07:34
Display posts from previous: Sort by