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A solution consists of only water and alcohol such that the

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A solution consists of only water and alcohol such that the

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e-GMAT

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 milliliters) so that the resulting solution contains 60% alcohol?

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

OA A.

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AAPL wrote:
e-GMAT

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 milliliters) so that the resulting solution contains 60% alcohol?

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

$$\left\{ \matrix{
\,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k \hfill \cr
\,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k + x \hfill \cr
\,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,\,\,\,{{7k} \over {10k + x}} = {3 \over 5}\,\,\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{{\rm{cross - multiply}}} \,\,\,\,\,\,5k = 3x\,\,\,\,\,\left( * \right)$$
$$? = x$$
$$\left( 1 \right)\,\,\,10k + x = 350\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,6x + x = 350\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\,$$
$$\left( 2 \right)\,\,{a \over w} = {{10.5} \over {4.5}}\,\,\left( { = {{105} \over {45}} = {7 \over 3}} \right)\,\,\,{\rm{already}}\,\,{\rm{known}}\,\,{\rm{pre - statements}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\,\,\,$$

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

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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AAPL wrote:
e-GMAT

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 milliliters) so that the resulting solution contains 60% alcohol?

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

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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