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GMAT Official Guide 2019 In a certain fraction, the

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by BTGmoderatorDC » Wed Jun 27, 2018 4:22 am

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Answers

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Difficulty—

In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?


A. 32

B. 64

C. 72

D. 80

E. 120
Last edited by BTGmoderatorDC on Sat Jun 30, 2018 11:11 pm, edited 2 times in total.
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by Brent@GMATPrepNow » Wed Jun 27, 2018 4:51 am
BTGmoderatorDC wrote:In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?


A. 32

B. 64

C. 72

D. 80

E. 120
Let N = the numerator
Let D = the denominator

...the denominator is 16 greater than the numerator.
We can write: D = N + 16

If the fraction is equivalent to 80 percent...
We can write: N/D = 80/100
Simplify to get: N/D = 4/5
Cross multiply to get: 5N = 4D

...what is the denominator of the fraction?
We now have the following system of equations
D = N + 16
5N = 4D

Take the top equation, and solve for N to get: N = D - 16
Now take the bottom equation and replace N with D - 16 to get: 5(D - 16) = 4D
Expand: 5D - 80 = 4D
Solve: D = 80

Answer: D

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Brent
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by [email protected] » Wed Jun 27, 2018 10:47 am
Hi All,

We're told that In a certain fraction, the denominator is 16 GREATER than the numerator and that the fraction is the equivalent to 80 percent. We're asked for the DENOMINATOR of the fraction. This question can be solved rathe easily by TESTing THE ANSWERS.

To start, we have...

numerator/denominator = .8

Between Answers B and D, Answer D is the easier option, so let's start there:

Answer D: 80
IF.... the denominator = 80, then we have....
(numerator)/80 = .8
(numerator) = (80)(.8) = 64
and the fraction becomes 64/80
The difference between the denominator and the numerator is 80 - 64 = 16. This is an exact match for what we were told, so this MUST be the answer.

Final Answer: D

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by Jeff@TargetTestPrep » Mon Jul 02, 2018 9:28 am
BTGmoderatorDC wrote:In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?


A. 32

B. 64

C. 72

D. 80

E. 120
Let n be the numerator of this expression. We can create the equation:

n/(n + 16) = 8/10

n/(n + 16) = 4/5

5n = 4n + 64

n = 64

Thus, the denominator is 64 + 16 = 80.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by Shahrukh_mbabreakspace » Tue Jul 03, 2018 2:02 am
Let the fraction be x/y
Since it is equivalent to 80%

Thus it is equal to 0.8
x/y= 0.8

and y-x= 16

On solving we get y=80

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