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# If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol  [#permalink]

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26 Nov 2019, 02:03
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:48) correct 36% (01:46) wrong based on 25 sessions

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If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol solution, what percentage of the final solution is alcohol?

(1) $$5x + 3y = 280$$
(2) $$2x + 7y = 460$$

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Joined: 19 Oct 2018
Posts: 1174
Location: India
Re: If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol  [#permalink]

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26 Nov 2019, 03:08
z is the percentage of resultant solution
z= 50x+30y/80

z=5x+3y/8

Statement 1= We know the value of 5x+3y
Sufficient

Statement 2-
We know the value of 2x+7y

We can't find 5x+3y using only 1 equation

Insufficient

Bunuel wrote:
If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol solution, what percentage of the final solution is alcohol?

(1) $$5x + 3y = 280$$
(2) $$2x + 7y = 460$$

Are You Up For the Challenge: 700 Level Questions
Director
Joined: 24 Nov 2016
Posts: 971
Location: United States
Re: If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol  [#permalink]

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26 Nov 2019, 04:54
Bunuel wrote:
If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol solution, what percentage of the final solution is alcohol?

(1) $$5x + 3y = 280$$
(2) $$2x + 7y = 460$$

(50x%+30y%)/80=z*100
([50x+30y]/100)/80=z*100
([50x+30y]/100)/80=z*100
[50x+30y]/80=z
5x+3y/8=z

(1) $$5x + 3y = 280$$ sufic

(2) $$2x + 7y = 460$$ insufic

Ans (A)
Senior Manager
Joined: 13 Feb 2018
Posts: 492
GMAT 1: 640 Q48 V28
Re: If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol  [#permalink]

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26 Nov 2019, 04:56
Amount of Alcohol in 50ml solution = $$\frac{50x}{100}$$
Amount of alcohol in 30ml solution = $$\frac{30y}{100}$$

Alcohol in mix = $$\frac{50x}{100}$$+$$\frac{30y}{100}$$=$$\frac{(5x+3y)}{10}$$
Total amount of mix =80

To find the percentage of alcohol in new solution we have to divide alcohol in mix by total amount of mix

1) Directly gives what we are looking for -- sufficient
2) From 2x+7y=460 we cant get the value of 5x+3y -- INsufficient

IMO
Ans: A
Re: If 50 mL of an x% alcohol solution is mixed with 30 mL of a y% alcohol   [#permalink] 26 Nov 2019, 04:56
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