In a certain fraction, the denominator is 16 greater than the numerator.

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

In a certain fraction, the denominator is 16 greater than the numerator.

by BTGModeratorVI » Mon Jun 22, 2020 6:11 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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Source: Beat The GMAT — Problem Solving | Mon Jun 22, 2020 6:11 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: In a certain fraction, the denominator is 16 greater than the numerator.

by Brent@GMATPrepNow » Tue Jun 23, 2020 2:44 pm

BTGModeratorVI wrote: ↑
Mon Jun 22, 2020 6:11 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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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: In a certain fraction, the denominator is 16 greater than the numerator.

by Scott@TargetTestPrep » Sat Jun 27, 2020 5:06 am

BTGModeratorVI wrote: ↑
Mon Jun 22, 2020 6:11 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

Solution:

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

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