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Posts: 26
Updated on: 24 Dec 2014, 01:00
Originally posted by Gmatdecoder on 23 Dec 2014, 22:31.
Last edited by Bunuel on 24 Dec 2014, 01:00, edited 1 time in total.
Last edited by Bunuel on 24 Dec 2014, 01:00, edited 1 time in total.
Edited the question.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
79% (01:38) correct
21%
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wrong
based on 650
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Two brands of detergent are to be combined. Detergent X contains 20 percent bleach and 80 percent soap, while Detergent Y contains 45 percent bleach and 55 percent soap. If the combined mixture is to be 35 percent bleach, what percent of the final mixture should be Detergent X?
(A) 10%
(B) 32 1/2 %
(C) 35%
(D) 40%
(E) 60%
(A) 10%
(B) 32 1/2 %
(C) 35%
(D) 40%
(E) 60%
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Gmatdecoder
Best is the allegation method. Refer diagram below:
Attachment:
ble.png [ 5.86 KiB | Viewed 21360 times ]
X percentage \(= \frac{10}{25} * 100 = 40%\)
Gmatdecoder
.2x+.45y=.35(x+y)
x/y=2/3
2/(3+2)=2/5=40%
General Discussion
Let we mix x units of detergent X and y units of detergent Y
Bleach Soap Total
Detergent X 0.20x 0.80x x
Detergent Y 0.45y 0.55y y
Combined 0.20x+0.45y 0.80x+0.55y x+y
Percentage of bleach in combined mixture = (0.20x+0.45y)/(x+y) = 35/100
20x + 45y = 35x + 35y
10y = 15x
x/y = 2/3
So, percentage of detergent x = x*100/(x+y) = (x/y)*100/ ((x/y)+1)
= (2/3)*100/((2/3)+1)
= 200/5 = 40%
So, Answer will be D
Hope it helps!
_________________
Bleach Soap Total
Detergent X 0.20x 0.80x x
Detergent Y 0.45y 0.55y y
Combined 0.20x+0.45y 0.80x+0.55y x+y
Percentage of bleach in combined mixture = (0.20x+0.45y)/(x+y) = 35/100
20x + 45y = 35x + 35y
10y = 15x
x/y = 2/3
So, percentage of detergent x = x*100/(x+y) = (x/y)*100/ ((x/y)+1)
= (2/3)*100/((2/3)+1)
= 200/5 = 40%
So, Answer will be D
Hope it helps!
Gmatdecoder
_________________
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Posts: 26
Please suggest simpler solution.
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Posted from my mobile device
EMPOWERgmatRichC
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Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
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Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
Hi Gmatdecoder,
In mixture questions, if you're not given amounts of each item to work with (in this case, the amount of the 2 detergents), then you can TEST VALUES and use real numbers to solve the problem.
Here, we're told about 2 detergents:
Detergent X = 20% bleach
Detergent Y = 45% bleach
We're told to mix some of each detergent together and end up with a 35% bleach mixture.
Here's how you can TEST VALUES:
Let's say you have 10 oz of Detergent X...
10(20%) = 2 oz bleach
We'll have to mix that with a certain amount of Detergent Y (let's call that Y oz.)
Y(45%) = .45Y oz bleach
Bleach/All = (2+.45Y)/(10 + Y) = .35
2+.45Y = 3.5 + .35Y
.1Y = 1.5
Y = 15
So, we need 15 oz. of Detergent Y to be mixed with 10 oz. of Detergent X to get a combined mixture that is 35% bleach.
The question asks what percent of the final mixture is X?
10/25 = 40%
Final Answer:
GMAT assassins aren't born, they're made,
Rich
In mixture questions, if you're not given amounts of each item to work with (in this case, the amount of the 2 detergents), then you can TEST VALUES and use real numbers to solve the problem.
Here, we're told about 2 detergents:
Detergent X = 20% bleach
Detergent Y = 45% bleach
We're told to mix some of each detergent together and end up with a 35% bleach mixture.
Here's how you can TEST VALUES:
Let's say you have 10 oz of Detergent X...
10(20%) = 2 oz bleach
We'll have to mix that with a certain amount of Detergent Y (let's call that Y oz.)
Y(45%) = .45Y oz bleach
Bleach/All = (2+.45Y)/(10 + Y) = .35
2+.45Y = 3.5 + .35Y
.1Y = 1.5
Y = 15
So, we need 15 oz. of Detergent Y to be mixed with 10 oz. of Detergent X to get a combined mixture that is 35% bleach.
The question asks what percent of the final mixture is X?
10/25 = 40%
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Posts: 1
How am I still not clear? Can someone simplify it further?
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