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# If the numerator of a fraction is decreased 25 percent and the denomi

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Math Expert
Joined: 02 Sep 2009
Posts: 51100
If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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18 Feb 2018, 22:10
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:45) correct 26% (01:57) wrong based on 53 sessions

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If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

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If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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18 Feb 2018, 22:14
Bunuel wrote:
If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

Let the original fraction will be $$\frac{x}{y}$$

If the numerator is decreased 25% and the denominator is increased 25%,
the resultant fraction becomes $$\frac{0.75x}{1.25y} = \frac{3}{5}*\frac{x}{y}$$(60% of its original value)

Therefore, the percentage decrease should be 40%(Option A)
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If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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20 Feb 2018, 00:34
Bunuel wrote:
If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

Assigning numbers here works well.

Original fraction
Use numbers that yield easy results when multiplied by $$\frac{3}{4}$$ (.75) and $$\frac{5}{4}$$ (1.25)

Let the original fraction = $$\frac{100}{100}$$ (which = 1)

New fraction
The numerator is decreased 25 percent. The denominator increases by 25 percent. New fraction:

$$\frac{75}{125}$$ (which =$$\frac{3}{5}$$)

Percent decrease?
Percent decrease generally:

$$\frac{|New-Old|}{Old}*100$$

Percent decrease here $$\frac{|\frac{3}{5}-1|}{1}*100)=(|-\frac{2}{5}|*100)=(0.4*100)=$$
40 percent decrease

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Posts: 2830
Re: If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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22 Feb 2018, 08:17
Bunuel wrote:
If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

We can let the original fraction = n/d and the new fraction = 0.75n/1.25d = (3n/4)/(5d/4) = 12n/20d = 3n/5d

Now we can determine the percent decrease:

[(3n/5d) - (5n/5d)]/(n/d) x 100

-2n/5d x d/n x 100 = -2/5 x 100 = -40, a 40% decrease

Alternate Solution:

Let’s let the original fraction be 1/1. When the numerator is decreased by 25% and the denominator is increased by 25%, the new fraction is 0.75/1.25 = 75/125 = 3/5.

We use the percent change formula (new - old)/old x 100%:

(3/5 -1)/1 x 100% = -2/5 x 100% = -40 percent, which is a 40% decrease.

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Re: If the numerator of a fraction is decreased 25 percent and the denomi &nbs [#permalink] 22 Feb 2018, 08:17
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