GMAT OFFICIAL GUIDE PS

Solution:

The first thing we want to do is set up the ratio of the original solution using variable multipliers.

soap : alcohol : water = 2x : 50x : 100x

We are given that the ratio of soap to alcohol is doubled. Our original ratio of soap to alcohol is:

soap/alcohol = 2x/50x = x/25x

(Notice that we only canceled the 2 and 50; we didn’t cancel the x because it’s our ratio multiplier.)

If we double the ratio we multiply the entire ratio by 2, so we have:

2(x/25x) = 2x/25x

So now our new ratio is:

soap/alcohol = 2x/25x

Next we are given that the ratio of soap to water is halved. Our original ratio of soap to water is:

soap/water = 2x/100x = x/50x

If we halve the ratio, we multiply the entire ratio by 1/2, so we have:

(1/2)(x/50x) = x/100x

So now our new ratio is:

soap/water = x/100x

Next we must notice that the amount of soap in the two new ratios is not the same value. In the first new ratio, soap = 2x and in the second new ratio, soap = x. Thus, we need to make these values equal before continuing to the answer. To do this, we multiply the second ratio by 2/2, so we have:

soap/water = (2/2)(x/100x) = 2x/200x

Now we can set up the ratio of the altered solution.

soap : alcohol : water = 2x : 25x : 200x

Lastly, we are given that the altered solution will contain 100 cubic centimeters of alcohol.

With this we can set up the following equation and determine x:

25x = 100

x = 4 (This means that the ratio multiplier is 4.)

Thus, the altered solution will contain (200)(4) = 800 cubic centimeters of water.

Answer: E

About The Author

Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.