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# The value of a fraction is 2/5. If the numerator is decreased by 2 and

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Math Expert
Joined: 02 Sep 2009
Posts: 56244
The value of a fraction is 2/5. If the numerator is decreased by 2 and  [#permalink]

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05 Mar 2018, 21:57
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35% (medium)

Question Stats:

76% (01:23) correct 24% (02:14) wrong based on 49 sessions

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The value of a fraction is 2/5. If the numerator is decreased by 2 and the denominator increased by 1, the resulting fraction is equivalent to 1/4. Find the numerator of the original
fraction.

(A) 3

(B) 4

(C) 6

(D) 10

(E) 15

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Re: The value of a fraction is 2/5. If the numerator is decreased by 2 and  [#permalink]

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05 Mar 2018, 22:54
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This problem is easiest to use back solving. First use the answer choices to get the original fraction. Then decrease the numerator by 2 and increase the denominator by 1. ***note that the original fraction is always simplifies to 2/5

a) Incorrect -- original fraction would be 3/7.5 >>> new fraction would be 1/8.5 which is not 1/4
b) Incorrect -- 4/10 >>> 2/11
C) Correct -- 6/15 >>> 4/16 which is equivalent to 1/4
D) Incorrect -- 10/25 >>> 8/26
E) Incorrect -- 15/37.5 >>> 13/38.5
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Re: The value of a fraction is 2/5. If the numerator is decreased by 2 and  [#permalink]

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05 Mar 2018, 23:29
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Bunuel wrote:
The value of a fraction is 2/5. If the numerator is decreased by 2 and the denominator increased by 1, the resulting fraction is equivalent to 1/4. Find the numerator of the original fraction.

(A) 3

(B) 4

(C) 6

(D) 10

(E) 15

Let the fraction be 2x/5x

If the numerator is decreased by 2 and the denominator increased by 1, the resulting fraction is equivalent to 1/4

(2x-2)/(5x+1) =(1/4)

On simplification x=3

So original numerator = 6

C
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Re: The value of a fraction is 2/5. If the numerator is decreased by 2 and  [#permalink]

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05 Mar 2018, 23:36
(A) 3 => 3/7.5 => 1/8.5 - Incorrect

(B) 4 => 4/10 => 2/11 - Incorrect

(C) 6 => 6/15 => 4/16 - Correct

(D) 10 =>10/25 =>8/26 - Incorrect

(E) 15 =>15/37.5 =>13/38.5 - Incorrect

Ans: C
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Re: The value of a fraction is 2/5. If the numerator is decreased by 2 and  [#permalink]

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08 Mar 2018, 11:39
Bunuel wrote:
The value of a fraction is 2/5. If the numerator is decreased by 2 and the denominator increased by 1, the resulting fraction is equivalent to 1/4. Find the numerator of the original
fraction.

(A) 3

(B) 4

(C) 6

(D) 10

(E) 15

Since the original fraction can be 2/5, 4/10 or any fraction that is equivalent to 2/5, we can let the original fraction be (2x)/(5x). Thus, we can create the following equation:

(2x - 2)/(5x + 1) = ¼

4(2x - 2) = 5x + 1

8x - 8 = 5x + 1

3x = 9

x = 3

Thus the numerator of the original fraction is 2(3) = 6.

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Re: The value of a fraction is 2/5. If the numerator is decreased by 2 and   [#permalink] 08 Mar 2018, 11:39
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