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

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Bunuel
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In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   19 Jun 2018, 21:36
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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

(PS00907)
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D
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   19 Jun 2018, 21:55
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Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)


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

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

Denominator = x + 16 = 64 + 16 = 80

Answer: D
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   19 Jun 2018, 23:13
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Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)



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
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   21 Jun 2018, 16:57
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Bunuel 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



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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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   24 May 2021, 04:36
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Video solution from Quant Reasoning:
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   19 Jun 2018, 23:16
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Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)



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
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   20 Jun 2018, 08:58
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nu is x+16/x=4/5 (80%).
We get equation => 5(x+16)=4x; 5x+80=4x; x=80
Hope it helps
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   27 Jun 2018, 05:57
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Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)


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
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   04 Aug 2019, 08:38
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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.

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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   02 Jul 2020, 07:37
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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.
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   20 Jun 2018, 11:12
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
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   26 Jan 2019, 17:42
Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)


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
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   15 Feb 2019, 00:46
Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)


Let numerator be x
denominator = x + 16

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

Denominator = 80

D
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   Updated on: 09 May 2021, 07:01
sydlyisaacs wrote:
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.


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

Originally posted by errorlogger on 17 Mar 2021, 14:31.
Last edited by errorlogger on 09 May 2021, 07:01, edited 1 time in total.
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   09 May 2021, 06:45
Expert Reply
Bunuel 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

NEW question from GMAT® Official Guide 2019


(PS00907)


Wanna make solving the Official Questions interesting???


Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
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Answer: Option D

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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   10 Feb 2023, 17:19
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
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Re: In a certain fraction, the denominator is 16 greater than the numerato [#permalink] New post   07 Apr 2024, 00:05
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