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

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In a certain fraction, the denominator is 16 greater than the numerato  [#permalink]

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New post 19 Jun 2018, 20:36
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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

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(PS00907)

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Re: In a certain fraction, the denominator is 16 greater than the numerato  [#permalink]

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New post 19 Jun 2018, 20:55
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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]

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New post 19 Jun 2018, 22:13
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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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In a certain fraction, the denominator is 16 greater than the numerato  [#permalink]

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New post 19 Jun 2018, 22:16
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]

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New post 20 Jun 2018, 07:58
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]

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New post 20 Jun 2018, 10:12
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]

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New post 21 Jun 2018, 15:57
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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]

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New post 27 Jun 2018, 04:57
Top Contributor
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 &nbs [#permalink] 27 Jun 2018, 04:57
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