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# Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3187
Location: India
GPA: 3.12
Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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03 Nov 2017, 09:56
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Difficulty:

15% (low)

Question Stats:

78% (01:39) correct 22% (02:25) wrong based on 130 sessions

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Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respectively. The four solutions are mixed in a proportion of 1:2:3:4 respectively. What will be the percentage of alcohol in the resultant solution?

A. 45%
B. 50%
C. 55%
D. 65%
E. 75%

Source: Experts Global

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Manager
Joined: 21 Jun 2014
Posts: 62
Re: Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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03 Nov 2017, 10:25
Just take out the weighted average. (20*1+40*2+50*3+100*4)/10
65%

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Senior Manager
Joined: 17 Oct 2016
Posts: 322
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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03 Nov 2017, 10:31
4
option D.

Concentration=(1*20+2*40+3*50+4*100)/(1+2+3+4)%
= 650/10%
=65%
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Help with kudos if u found the post useful. Thanks

Manager
Joined: 04 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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14 Nov 2017, 03:20
1
1
Ratio=1:2:3:4 ie the quantity is in this ratio
if A=100 ml than B=200ml, C=300ml, and D=400ml as per above ratio
In A % of alcohol is 20% ie in 100ml=20ml, similarly % of alcohol in B is 40%=80ml, C is 50%=150ml and D is 100%=400ml
Total alcohol is =A+B+C+D=20+80+150+400=650ml
Total solution=100+200+300+400=1000ml
% of alcohol=(650/1000)*100=65% Ans D.
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Re: Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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02 Dec 2017, 19:40
why people in this post receive so many kudos even though the math problem is not hard at all?
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Joined: 02 Aug 2009
Posts: 6960
Re: Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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02 Dec 2017, 20:17
1
pushpitkc wrote:
Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respectively. The four solutions are mixed in a proportion of 1:2:3:4 respectively. What will be the percentage of alcohol in the resultant solution?

A. 45%
B. 50%
C. 55%
D. 65%
E. 75%

Source: Experts Global

Ofcourse the straight method is given..
Merely looking at the concentration and ratio should get you to the answer.
1) 75% can be ruled out as then 50% and 100% should have equal proportions. But 50% and below is 1+2+3=6 parts and 100% is 4 parts so answer < 75%
2) 20:40:50 are in ratio 1:2:3 so the ratio is more towards 50%..
The combined 6 parts of 20,40 and 50% has to be more than 40.
So 6 parts of 40 and 4 part of 100 will get you 100-6*60/10=100-36=64

Only 65% is left
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Re: Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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02 Dec 2017, 20:29
chesstitans wrote:
why people in this post receive so many kudos even though the math problem is not hard at all?

the post helped me so i will complement it with kudos
Not everybody is at the same level and to assume that something is easy for you will be easy for others is a "flaw in the reasoning"
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Joined: 22 May 2016
Posts: 2034
Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective  [#permalink]

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06 Dec 2017, 14:23
pushpitkc wrote:
Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respectively. The four solutions are mixed in a proportion of 1:2:3:4 respectively. What will be the percentage of alcohol in the resultant solution?

A. 45%
B. 50%
C. 55%
D. 65%
E. 75%

Source: Experts Global

Four solutions. Different concentrations of alcohol. Different amounts (volumes) of each mixed. Result: final solution of $$x$$ percent alcohol.

Known quantities (do not get an "x" in the equation*):
--The 4 solutions' alcohol concentrations and volume
--total resultant mix's volume (amount)

Unknown quantity: resultant mix's concentration of alcohol

Decimal percentages = alcohol concentrations (100% = 100/100 = 1)
$$.20(1) + .40(2) + .50(3) + 1(4) =\frac{x}{100}(1+2+3+4)$$

$$.20 + .80 + 1.5 + 4 = \frac{x}{100}(10)$$
$$6.5 = \frac{x}{100}(10)$$
$$\frac{6.5}{10}=\frac{x}{100}$$
$$.65(100) = x$$
$$x = 65$$
percent

*Let different solutions = A, B, C, D, etc. There can be as many as needed in the equation below

1) multiply A's concentration by A's volume, and
2) do the same for each solution; then
3) add all of them (LHS); to yield
3) both resultant volume and resultant concentration (RHS)

$$(Conc_{A})(Vol_{A}) + (Conc_{B})(Vol_{B})=(Conc_{A+B})(Vol_{A+B})$$

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Solutions A,B,C,and D contain 20%,40%,50%, and 100% alcohol respective &nbs [#permalink] 06 Dec 2017, 14:23
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