Hi,
The answer to this is E) but could not figure why...Can anyone please explain?
A certain fraction is equivalent to 2/5 . If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3 . What is the sum of the numerator and denominator of the original fraction?
(A) 49 (B) 35 (C) 28
(D) 26 (E) 21
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jayhawk2001
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Original fraction --
x/y = 2/5
5x = 2y
Modified fraction --
(x+4) / 2y = 1/3
3x + 12 = 2y
5x = 3x + 12
x = 6
So y = 15
x + y = 21
x/y = 2/5
5x = 2y
Modified fraction --
(x+4) / 2y = 1/3
3x + 12 = 2y
5x = 3x + 12
x = 6
So y = 15
x + y = 21
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Cybermusings
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x/y = 2/5
5x-2y=0 --------- 1)
x+4/2y = 1/3
3x+12=2y
3x-2y= -12 ------------- 2)
After solving the two simultaneously you get x = 6 and y = 15
Sum of the 2 = 6+15 = 21
5x-2y=0 --------- 1)
x+4/2y = 1/3
3x+12=2y
3x-2y= -12 ------------- 2)
After solving the two simultaneously you get x = 6 and y = 15
Sum of the 2 = 6+15 = 21
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BTGmoderatorRO
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let the numerator and denominator of the fraction be x and y respectively
$$\frac{x}{y}$$ = $$\frac{2}{5}$$ .....eqn 1
If x is increased bt 4 i.e x+4, and y is doubled i.e 2y
$$\frac{x+4}{2y}$$ = $$\frac{1}{3}$$ .....eqn 2
$$3\left(x+4\right)$$ = 2y
3x-2y=-12\
From eqn 1
5x-2y=0
Solving these equations simultaneously,
3x-2y=-12
- 5x-2y=0
___________________________
-2x=-12
= $$\frac{-12}{-2}$$ =6
Thertefore, x=6
and 3(6)-2y=-12
Therfore,y=15
The original fraction is $$\frac{6}{15}$$
and the sum of x and y is
6+15 = 21.
$$\frac{x}{y}$$ = $$\frac{2}{5}$$ .....eqn 1
If x is increased bt 4 i.e x+4, and y is doubled i.e 2y
$$\frac{x+4}{2y}$$ = $$\frac{1}{3}$$ .....eqn 2
$$3\left(x+4\right)$$ = 2y
3x-2y=-12\
From eqn 1
5x-2y=0
Solving these equations simultaneously,
3x-2y=-12
- 5x-2y=0
___________________________
-2x=-12
= $$\frac{-12}{-2}$$ =6
Thertefore, x=6
and 3(6)-2y=-12
Therfore,y=15
The original fraction is $$\frac{6}{15}$$
and the sum of x and y is
6+15 = 21.
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Hi All,
We're told that a certain fraction is equivalent to 2/5, the numerator of the fraction is increased by 4 and the denominator is doubled, so the new fraction is equivalent to 1/3 . We're asked for the SUM of the numerator and denominator of the ORIGINAL fraction. This question can be solved in a couple of different ways; here's how you can solve it with a bit of 'brute force' arithmetic.
Since the original fraction = 2/5, that fraction could be... 2/5, 4/10, 6/15, 8/20, 10/25 etc. The answer choices are relatively small, so we can 'test out' the options until we find the one that 'fits' all of the information we were given....
IF... we're dealing with 2/5... then the 'new' number will be 6/10. That is NOT 1/3, so the original fraction is NOT 2/5
IF... we're dealing with 4/10... then the 'new' number will be 8/20. That is NOT 1/3, so the original fraction is NOT 4/10
IF... we're dealing with 6/15... then the 'new' number will be 10/30. That IS 1/3, so the original fraction IS 6/15. Thus, the answer to the question is 6+15 = 21
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that a certain fraction is equivalent to 2/5, the numerator of the fraction is increased by 4 and the denominator is doubled, so the new fraction is equivalent to 1/3 . We're asked for the SUM of the numerator and denominator of the ORIGINAL fraction. This question can be solved in a couple of different ways; here's how you can solve it with a bit of 'brute force' arithmetic.
Since the original fraction = 2/5, that fraction could be... 2/5, 4/10, 6/15, 8/20, 10/25 etc. The answer choices are relatively small, so we can 'test out' the options until we find the one that 'fits' all of the information we were given....
IF... we're dealing with 2/5... then the 'new' number will be 6/10. That is NOT 1/3, so the original fraction is NOT 2/5
IF... we're dealing with 4/10... then the 'new' number will be 8/20. That is NOT 1/3, so the original fraction is NOT 4/10
IF... we're dealing with 6/15... then the 'new' number will be 10/30. That IS 1/3, so the original fraction IS 6/15. Thus, the answer to the question is 6+15 = 21
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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We can let the fraction = 2x/5x and create the equation:dunkin77 wrote:Hi,
The answer to this is E) but could not figure why...Can anyone please explain?
A certain fraction is equivalent to 2/5 . If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3 . What is the sum of the numerator and denominator of the original fraction?
(A) 49 (B) 35 (C) 28
(D) 26 (E) 21
(2x + 4)/(10x) = 1/3
3(2x + 4) = 10x
6x + 12 = 10x
12 = 4x
3 = x
Thus the numerator and denominator of the original fraction are 2(3) = 6 and 5(3) = 15, respectively, yielding a sum of 6 + 15 = 21.
Answer: E
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