AustinKL wrote:

There are 2 circular cylinders X and Y, and both cylinders contain water inside. Cylinder X has \(5π\) square inches as the base area and 6 inches as the height of the water inside, and cylinder Y has \(10π\) square inches as the base area and 2 inches as the height of the water inside. If the height of the water becomes the same when the water drawn from cylinder X is poured into cylinder Y, what is the height of water in these cylinders, in inches?

A. 2.5

B. 3

C. \(\frac{10}{3}\)

D. 4

E. 4.5

First let’s determine the volume of water in each of the two cylinders before water from one is poured into the other. Recall that the volume of a cylinder is V = Bh, in which B is the circular base area and h is the height of the cylinder. Thus we have:

Water in cylinder X: Volume = 5? x 6 = 30? in^3

Water in cylinder Y: Volume = 10? x 2 = 20? in^3

Now we can let w be the amount of water that should be poured from cylinder X to cylinder Y so that the water in both cylinders will be the same height. Notice that if V = Bh, then h = V/B.

Thus we have:

(30? - w)/5? = (20? + w)/10?

5?(20? + w) = 10?(30? - w)

100?^2 + 5w? = 300?^2 - 10w?

15w? = 200?^2

3w = 40?

w = 40?/3

Since w = 40?/3, the height of water in each cylinder is:

(30? - 40?/3)/5?

(90? - 40?)/15?

50?/15? = 10/3

Answer: C

_________________

Scott Woodbury-Stewart

Founder and CEO

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions