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

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by BTGModeratorVI » Sun Aug 02, 2020 7:03 am

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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

Answer: D
Source: Official guide
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Re: In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent

by Brent@GMATPrepNow » Sun Aug 02, 2020 10:58 am
BTGModeratorVI wrote: ↑
Sun Aug 02, 2020 7:03 am
 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

Answer: D
Source: Official guide
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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