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A certain 4-liter solution of water, vinegar, and alcohol consists of

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A certain 4-liter solution of water, vinegar, and alcohol consists of  [#permalink]

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New post 19 Apr 2019, 04:08
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:14) correct 17% (01:41) wrong based on 24 sessions

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A certain 4-liter solution of water, vinegar, and alcohol consists of x liters of water, y liters of vinegar, and z liters of alcohol.
How many liters of water does the solution contain?

(1) The ratio of water to vinegar is 4 : 1.
(2) The ratio of vinegar to alcohol is 3 : 1
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A certain 4-liter solution of water, vinegar, and alcohol consists of  [#permalink]

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New post 19 Apr 2019, 05:26
1
From question we can conclude that x+y+z=4

(1)From Option1 x/y = 4/1, but without the value of alcohol we cannot calculate the amount of water in the solution, so it's INSUFFICIENT
(2)From Option1 y/z = 3/1, but without the value of water we cannot calculate the amount of water in the solution, so it's INSUFFICIENT

But by combining both and multiplying 1st equation by 3 we get

x:y:z = 12:3:1

so x+y+z=4
=> 16z=40
=> z=40/16 from which we can find x.
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Re: A certain 4-liter solution of water, vinegar, and alcohol consists of  [#permalink]

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New post 19 Apr 2019, 06:18
1
(1) Water:Vinegar= 4:1 , this does not tell us the relation to alcohol and hence is clearly insufficient. Cross off both A,D

(2) Vinegar: Alcohol= 3:1, this again tells nothing about Water content in solution. So cross Off B . Now either C or E can be the answer.

Consider both (1) and (2) together

Water: Vinegar= 4:1= 12:3
Vinegar:Alcohol= 3:1

Hence, clearly we have Water :Vinegar: Alcohol = 12::3:1 . This will give us a unique solution for water content = 3 litres

Hence, the answer is C
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Re: A certain 4-liter solution of water, vinegar, and alcohol consists of  [#permalink]

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New post 19 Apr 2019, 06:29
1
OA:C

Amount of water in solution = \(x\) liters
Amount of vinegar in solution = \(y\) liters
Amount of alcohol in solution = \(z\) liters

Given: \(x+y+z=4\quad\)...(1)

(1) The ratio of water to vinegar is \(4: 1\).

\(\frac{x}{y}=\frac{4}{1}\)

\(y=\frac{x}{4}\quad\) ...(2)

Putting (2) into (1), we get

\(x+\frac{x}{4}+z=4\)

\(\frac{5x}{4}+z=4\)

As we do not know the relationship between \(x\) and \(z\) or relationship between \(y\) and \(z\) or value of \(z\), We cannot get the value of \(x\).

So Statement \(1\) alone is insufficient.

(2) The ratio of vinegar to alcohol is \(3 : 1\)

\(\frac{y}{z}=\frac{3}{1}\)

\(z=\frac{y}{3}\quad\) ...(3)

Putting (3) into (1), we get

\(x+y+\frac{y}{3}=4\)

\(x+ \frac{4y}{3}=4\)

As we do not know the relationship between \(x\) and \(y\) or \(x\) and \(z\) or value of \(y\), We cannot get the value of \(x\).

So Statement \(2\) alone is insufficient.

Combining Statement (1) and Statement (2), we get

\(y=\frac{x}{4}\quad\) ...(2)
\(z=\frac{y}{3}\quad\) ...(3)

Putting the value of \(y\) from (2) into (3), we get
\(z=\frac{\frac{x}{4}}{3}=\frac{x}{12}\quad\) ...(4)

Putting the value of \(y\) from (2) and value of \(z\) from (4) into (1), we get

\(x+\frac{x}{4}+\frac{x}{12}=4\quad\)
\(\frac{16x}{12}=4\quad\)
\(x=\frac{12*4}{16}=3\)
Combining Statement (1) and Statement (2), We are able to get the value of \(x\)
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Re: A certain 4-liter solution of water, vinegar, and alcohol consists of  [#permalink]

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New post 19 Apr 2019, 09:29
Statement (1) doesn’t provide that: the ratio of water to vinegar is helpful, but without knowing how alcohol fits into the picture, we can’t answer the question.
Statement (2) has a similar problem: it gives us the relationship between vinegar and alcohol, but nothing about their relationship with water.
Taken together, the statements are sufficient
we have three equations involving the three variables. and we can solve the question
So answer is C
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Re: A certain 4-liter solution of water, vinegar, and alcohol consists of   [#permalink] 19 Apr 2019, 09:29
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