Word Problem - A solution consists of only water and alcohol such that

Question

Q.)
A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in mililiters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 mililiters.
2. The original solution contains 10.5 mililiters of alcohol for every 4.5 mililiters of water.

Thanks,
Saquib
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TheMechanic · Accepted Answer

A simple solution to this could be: C1 x V1 (initial) = C2 x V2 (final)

We are given, for concentration of alcohol: 
C1 = 70%
C2 = 60%.

Using Statement 1: We get V2= 350lits.
Putting this in above equation, 
we get V1 = 60 x 350/70 = 300 lits.

Hence the water that was added is 50 lits.

Stmt 1 is sufficient.

Stmt 2: It simply re-states the ratio of concentration of Alcohol and Water in actual quantities. It does not give any new relation. Hence it is not sufficient.

The answer is A.

I hope this helps.

EgmatQuantExpert · Answer

Solution

Step 1 & Step 2: Understanding the Question statement and Drawing Inferences

Given info:

⇒ Quantity of alcohol = \(\frac{7\mathrm x}{10}\)
⇒ Quantity of water = \(\frac{3\mathrm x}{10}\)

To find:

⇒ \(\frac{\frac{7\mathrm x}{10}}{(\mathrm x+\mathrm y)}\ast100=60\)
⇒ \(\frac{\frac{7\mathrm x}{10}}{(\mathrm x+\mathrm y)}=\frac35\)
Multiplying both sides of the equation by 5, we get
⇒ \(\frac{\left(\frac{7\mathrm x}{10}\right)\ast5}{(\mathrm x+\mathrm y)}=3\)
⇒ \(\frac{\left(\frac{7\mathrm x}2\right)}{(\mathrm x+\mathrm y)}=3\)
⇒\(3.5x = 3x+3y\)
⇒\(0.5x = 3y\) ...(Equation 1)

Step 3: Analyze statement 1 independently

⇒ \(x+y=350ml\) ...(Equation 2)

statement 1 is sufficient

Step 4: Analyze statement 2 independently

statement 2 is not sufficient

Step 5: Analyze the two statements together

Option A

Thanks,
Saquib
Quant Expert
e-GMAT

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EgmatQuantExpert · Answer

The official solution has been posted. Looking forward to a healthy discussion..

rohit8865 · Answer

(in 350 ml --> 245 ml is alcohol + 105ml is water(given ratio 7:3)
let w be the quantity of water added to be 40% water(or 60% alcohol) in final solution
 thus 105 +w =40%(350+w)
thus w can be calculated
suff

(2) ony gives ratio 10.5/4.5= 7/3 which is given in question
No idea of volume...
insuff

Ans A

Madhavi1990 · Answer

Did it in 2:30 minutes (i guess way over time)
a/w = 7/3 (total parts 10)
we need a/w = 6/4

1) total ML is 350 --> easily we will know 350/10 = 35, divided each into 6/4 ratios. So exact amount of a/w can be achieved.

2) ratio of a/w= 10.5/ 4.5 --> great, but this would apply to each part of the mixture. How do we know the total milliliters? Hence insuff.

Ans A

fskilnik · Answer

In the solution below, the unit considered is always milliliters.

Let´s use the  k technique , one of the best tools of our method when dealing with ratios/proportions!

\left\{ \matrix{
 \,{m{water}}\,\,\left( w ight)\,\,\, = \,\,3k \hfill \cr 
 \,{m{alcohol}}\,\,\left( a ight) = 7k \hfill \cr} ight.\,\,\,\,\,\,\left( {k > 0} ight)\,\,\,\,\,\,\,\,\,\,\, 	o \,\,\,\,\,\,\,\,\,\left\{ \matrix{
 \,{m{water}}\,\,\left( w ight)\,\,\, = \,\,3k + x \hfill \cr 
 \,{m{alcohol}}\,\,\left( a ight) = 7k \hfill \cr} ight.\,\,\,\,\,\,\,{m{such}}\,\,{m{that}}\,\,\,\,\,\,{{7k} \over {10k + x}} = {3 \over 5}\,\,\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{{m{cross - multiply}}} \,\,\,\,\,\,5k = 3x\,\,\,\,\,\left( * ight)

? = x

\left( 1 ight)\,\,\,10k + x = 350\,\,\,\,\mathop \Rightarrow \limits^{\left( * ight)} \,\,\,\,\,6x + x = 350\,\,\,\,\, \Rightarrow \,\,\,\,\,{m{SUFF}}.\,\,\,\,\,\,\,

\left( 2 ight)\,\,{a \over w} = {{10.5} \over {4.5}}\,\,\left( { = {{105} \over {45}} = {7 \over 3}} ight)\,\,\,{m{already}}\,\,{m{known}}\,\,{m{pre - statements}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{m{INSUFF}}.\,\,\,

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

prvarm24 · Answer

A - sufficient 
B - mistakanely considered it as sufficient - missed that its the same information as metnioned in the question - no new information

ScottTargetTestPrep · Answer

We can let the amount of water to be added be w and the original amount of alcohol and water be 7x and 3x, respectively. We can create the equation:

(3x + w)/(7x + 3x + w) = 6/10

(3x + w)/(10x + w) = 3/5

5(3x + w) = 3(10x + w)

15x + 5w = 30x + 3w

2w = 15x

We need to determine the value of w. We see that w = 15x/2 or x = 2w/15. Therefore, if we know one of the two variables, then we know the other.

Statement One Only:

Total quantity of the resulting solution is 350 milliliters.

This means 10x + w = 350. Since x = 2w/15, we have:

10(2w/15) + w = 350

4w/3 + w = 350

4w + 3w = 1050

7w = 1050

w = 150

Statement one alone is sufficient.

Statement Two Only:

The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.

This means original amount of alcohol and water are 10.5y and 4.5y, respectively. Therefore, we have:
 
7x = 10.5y and 3x = 4.5y

Either way, we have x = 1.5y. However, since y can be any positive number (for example, if y = 2, then x = 3 and if y = 4, then x = 6), we can’t determine a unique value of x, and therefore, we can’t determine the value of w. Statement two alone is not sufficient.

Answer: A

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Word Problem - A solution consists of only water and alcohol such that

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