In a certain fraction, the denominator is 16 greater than the numerato

Question

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

(PS00907)

alldaytestprep · Accepted Answer

\frac{x}{x+16}  =  \frac{80}{100}  = 4/5

Cross Multiply to Get:
4x + 64 = 5x ---> x = 64

Denominator = x + 16 = 64 + 16 = 80

Answer: D

chetan2u · Answer

Various ways..

1) 80% means 80 out of 100, so here 80 is 100-80=20 less than 100
But we are looking for 16 less...
Difference is 20, denominator is 100..
So when difference is 16, denominator will be  \frac{100}{20}*16=80

2) let numerator be X, so denominator will be X+16
So  \frac{X}{X+16}=\frac{80}{100}....100X=80X+16*80....20X=16*80....X=16*4=64 
Therefore X+16=64+16=80..

3) substitution
Substitute denominator as per the choices and see what corresponds to 80%
Always better to start with MIDDLE value so that you minimize your task..
If C<80% check for D and E
If C>80%, check for B and A
If C=80% that is your answer
C. 72
Fraction =  \frac{72-16}{72}=56/72=7/9 < 8/10 
So check for D
D. 80
(80-16)/80=64/80=8/10.. YES

D

pushpitkc · Answer

Alternate approach

If denominator of fraction is x, we can evaluate the answer options and check which
of the fractions yield 80% | For denominator x ->  \frac{x-16}{x}  must be equal to  \frac{4}{5}

A.  32 = \frac{32-16}{32} = \frac{16}{32} = \frac{1}{2} 
B.  64 = \frac{64-16}{64} = \frac{48}{64} = \frac{3}{4} 
C.  72 = \frac{72-16}{72} = \frac{56}{72} = \frac{7}{9} 
  D.  80 = \frac{80-16}{80} = \frac{64}{80} = \frac{4}{5} 
  E.  120 = \frac{120-16}{120} = \frac{104}{120} = \frac{13}{15} 
 
Therefore,  Option D(80)  is the value for the denominator of the fraction

nigina93 · Answer

nu is x+16/x=4/5 (80%). 
We get equation => 5(x+16)=4x; 5x+80=4x; x=80
Hope it helps

pikolo2510 · Answer

x/x+16 = 4/5

there denominator has to be a multiple of 5. A,B, and C are out

when denominator is 80 i.e. when the ratio 4/5 is multiplied by 16. Numerator will become 64. therefor the ratio will be 64/80

Satisfies the condition. hence answer is D

ScottTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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

Jsound996 · Answer

What are we solving for: The value of the Denominator 
Value for Numerator: (n)
 Value for Denominator: (n+16)

(n)/(n+16) = 80/100
(n)/(n+16) = 4/5
5n = 4(n+16)
5n = 4n + 64
n = 64

(64+ 16) = 80

Answer is D

KanishkM · Answer

Let numerator be x
denominator = x + 16

x/x+16 = 4/5
5x -4x = 64
x = 64

Denominator = 80

D

RashedVai · Answer

lets try less math and more logic!

We know 80% = 4/5 --> the difference between denominator and numerator is 1. 
We are said that the difference is 16.
So, if 1 is to 16,
Then 5 is to 80. Or,
 1/16 = 5/x
 x = 80

Happy studying.

Posted from my mobile device

sydlyisaacs · Answer

This is a general issue that became apparent in this problem for me, but I just spent WAY TOO LONG on this problem because no matter how many times I read and re-read the question, my brain kept inserting "16 times greater" into the problem instead of the "16 greater". And the thing is, this is the second time I'm doing this problem. I did this problem in a first round of studying months ago and I did the SAME EXACT THING. Does anyone have any tips on how to just read the damn question correctly? It's insane. Re-reading and reading slowly don't seem to work.

errorlogger · Answer

You have already highlighted the pattern to your problem. If I were you, I would stop each time I see something like 'X is 5 greater than Y'
or something similar. One more thing, try converting words into equation and that should help.
50 is ten times 5.
=>50 =(is) 10 X(times) 5.
+>50 = 10X5.
Similarly, 10 is 5 greater than 5.
10 = 5 + 5

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=-b2sEa8UOxs

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=XpJ53KZmnPw

HoudaSR · Answer

80%=8/10=4/5. The denominator must be a multiple of 5.
By looking at the answer choices, only D and E are possible answer choices.
Let's take D= 80, 80/5= 16. if we multiply the numerator by 16, we get: 16x4=64
80-64=16. 
Hence the correct answer is D.80

bumpbot · Answer

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In a certain fraction, the denominator is 16 greater than the numerato

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