500 ps test22 # 17

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

500 ps test22 # 17

by dunkin77 » Sun Apr 15, 2007 10:29 am

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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Source: Beat The GMAT — Problem Solving | Sun Apr 15, 2007 10:29 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pm; Location: Silicon valley, California; Thanked: 30 times; Followed by:1 members

by jayhawk2001 » Sun Apr 15, 2007 12:34 pm

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

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Wed Apr 18, 2007 3:01 am

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

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

by BTGmoderatorRO » Sat Dec 09, 2017 10:14 am

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.

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by [email protected] » Sat Dec 09, 2017 2:21 pm

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

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Sun Sep 29, 2019 6:02 pm

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

We can let the fraction = 2x/5x and create the equation:

(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

Scott Woodbury-Stewart
Founder and CEO
[email protected]