GMAT OFFICIAL GUIDE PS

Solution:

We are given a rectangular solid and also are given areas of three of the sides. Let’s draw the figure out. We label the length, width, and height. We also label each side as side A, side B, and side C.

In the rectangular solid above, the three sides shown...

We see that the area of side A is length times height, that of side B is length times width, and that of side C is height times width.

We are given that the sides have areas of 12, 15, and 20.

Let’s say:

Side A area = 20

Thus we can set up the following equation for area:

length x height = 20

Side B area = 15

Thus we can set up the following equation for area:

length x width = 15

Side C area = 12

height x width = 12

Analyzing the two equations, length x height = 20 and length x width = 15, we see that both 15 and 20 are multiples of 5 and we also see that each equation contains the common term of “length”. Thus, we can deduce that the length could equal 5. When length is 5, we see height is 4, and when length is 5, we see that width is 3. We now have our dimensions for length, width, and height.

length = 5

width = 4

height = 3

Since volume of a rectangular solid = length x width x height, the volume is:

5 x 4 x 3 = 60.

Answer: A

(Note: If we were struggling to know which sides were sides A, B, and C, we could have selected those sides in any order and we would have ended up with the same value for the volume. If that were not the case, we would have to have been given more specific instructions about which sides corresponded to which areas.)

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.