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# A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5

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CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City
A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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24 Nov 2007, 02:18
2
KUDOS
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25% (medium)

Question Stats:

75% (02:32) correct 25% (01:42) wrong based on 225 sessions

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A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Oct 2014, 06:19, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
SVP
Joined: 29 Aug 2007
Posts: 2473
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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24 Nov 2007, 02:44
1
KUDOS
bmwhype2 wrote:
A 50 liter solution of alcohol and water is 5% alcohol. If 1.5 liters of alcohol and 8.5 liters are added to the solution, what percent of the solution produced is alcohol?

= 4/60
= 1/15
= 6.67%
Intern
Joined: 06 Nov 2004
Posts: 11
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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24 Nov 2007, 15:11
1
KUDOS
I disagree

50L * .05 = 2.5 L of alc, 50L - 2.5L = 47.5L of water

2.5 + 1.5 = 4L of alcohol in new solution

47.5L + 8.5L = 56L of water

4L / 56L = 1/14

this is ~7%
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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24 Nov 2007, 15:25
1
KUDOS
Expert's post
C1=Va/(Va+Vw) where, C -concentration; Va - volume of alcohol, Vm - volume of water. Vtotal=(Va+Vw) - total volume.

C1=Va/(Va+Vw)

C2=(Va+dVa)/(Va+Vw+dVa+dVw) where dVa - additional volume of alcohol, dVm - additional volume of water

C2=(C1*Vtotal+dVa)/(Vtotal+dVa+dVw)

C2=(0.05*50+1.5)/(50+1.5+8.5)=4/60=1/15~0.06666666 ==>6,(6)%
CEO
Joined: 21 Jan 2007
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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30 Nov 2007, 11:39
GMAT TIGER wrote:
bmwhype2 wrote:
A 50 liter solution of alcohol and water is 5% alcohol. If 1.5 liters of alcohol and 8.5 liters are added to the solution, what percent of the solution produced is alcohol?

= 4/60
= 1/15
= 6.67%

5% of 50 = 2.5 liters of alcohol

50+10=60

2.5+1.5=4

4/60=2/30=1/15=6.67%
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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30 Nov 2007, 11:40
Dakinemon wrote:
I disagree

50L * .05 = 2.5 L of alc, 50L - 2.5L = 47.5L of water

2.5 + 1.5 = 4L of alcohol in new solution

47.5L + 8.5L = 56L of water

4L / 56L = 1/14

this is ~7%

u took the percentage of alcohol from total water
Q asked for percentage of alcohol from total solution
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Joined: 09 Sep 2013
Posts: 15929
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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24 Oct 2014, 09:55
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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02 Apr 2016, 12:19
5% alcohol in 50 litre solution = 2.5 litres
adding 1.5 litres to it makes it total of 4 litres
total solution = 60 litres
% alcohol = 4/60 * 100 = 6.666667%
Director
Joined: 07 Dec 2014
Posts: 710
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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02 Apr 2016, 14:00
let x=% of alcohol in final solution
2.5+1.5=60x
x=1/15=6 2/3%
Manager
Joined: 19 Mar 2014
Posts: 173
Location: United States
Concentration: Finance, Entrepreneurship
Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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23 Jun 2017, 15:11
I am not clear on this question, shouldn't the answer be 7%?

As new solution will be 4 Ltrs Alcohol & 56 Ltrs of Water = 60 in Total

$$4/60*100 = 6.66$$

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Manager
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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23 Jun 2017, 15:34
ydmuley

A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution,
what percent of the solution produced is alcohol?

we are asked to find the exact percent- why are you rounding off the value?

$$\frac{4}{60}$$ * 100 = $$\frac{20}{3}$$ = 6 $$\frac{2}{3}$$ = Ans is D
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Schools: ISB '19, IIMA , IIMB, XLRI
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A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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23 Jun 2017, 15:35
bmwhype2 wrote:
A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%

Solution $$= 50$$ liters

Alcohol is 5% of 50 $$= \frac{5}{100} * 50 = 2.5$$ liters

1.5 liters of alcohol added. Therefore Total liters of alcohol $$= 2.5 + 1.5 = 4$$ liters.

1.5 liters of alcohol and 8.5 liters of water is added to solution $$= 50 + 1.5 + 8.5 = 60$$ liters.

Percentage of alcohol in new solution $$= \frac{4}{60} * 100 = 66.67$$% or $$6 \frac{2}{3}$$ % . Answer (D) ...
Manager
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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23 Jun 2017, 15:40
sashiim20 wrote:
bmwhype2 wrote:
A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%

Solution $$= 50$$ liters

Alcohol is 5% of 50 $$= \frac{5}{100} * 50 = 2.5$$ liters

1.5 liters of alcohol added. Therefore Total liters of alcohol $$= 2.5 + 1.5 = 4$$ liters.

1.5 liters of alcohol and 8.5 liters added to solution $$= 50 + 1.5 + 8.5 = 60$$ liters.

Percentage of alcohol in new solution $$= \frac{4}{60} * 100 = 66.67$$% or $$6 \frac{2}{3}$$ % . Answer (D) ...

Once again thanks for the explanation, it was helpful. Where I went wrong is incorrectly reading option C & D as $$62/3$$ and $$61/3$$

Hence, I was left with option E which was more closer to the number.

Good one
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Manager
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]

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23 Jun 2017, 15:44
Leo8 wrote:
ydmuley

A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution,
what percent of the solution produced is alcohol?

we are asked to find the exact percent- why are you rounding off the value?

$$\frac{4}{60}$$ * 100 = $$\frac{20}{3}$$ = 6 $$\frac{2}{3}$$ = Ans is D

Got it Leo8 - Thank you. I misread the answer choices as 61/3 & 62/3
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Kudos - I hope you liked the post, if you have liked the post, please do not hesitate to show your appreciation and support with a simple click on Kudos, it will make me happy and encourage me to support more people.

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5   [#permalink] 23 Jun 2017, 15:44
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