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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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