Is the number of members of Club

Varun Reddy

How is it that overlap equals 0.2x=0.3y ? Shouldnt it be 0.2x + 0.3y = overlap

Jun 26, 2017 • Reply

Sam Kinsman, Magoosh Tutor

Hi Varun,

Happy to help! Let's take a look at the statements:

(1) Of the members of Club X, 20 percent are also members of Club Y.
(2) Of the members of Club Y, 30 percent are also members of Club X.

To make things easier, let's call the overlap region "K." So K denotes the people that are both in club X and in club Y.

From statement 1, we know that 20% of the members in club X are also in club Y. So we know that 0.2*X = the overlap, or 0.2*X = K.

From statement 2, we know that 30% of the members in club Y are also in club X. So we know that 0.3*Y = the overlap, or 0.3*Y = K.

So there are two ways that we can express K. We know that 0.2*X = K, and we know that 0.3*Y = K. So we don't need to add 0.2*X and 0.3*Y. Instead, we can say:

0.2*X = K
0.3*Y = K

0.2*X = K = 0.3*Y

0.2*X = 0.3*Y = K

0.2*X = 0.3*Y

I hope this clarifies! :)

Best,
Sam

Jul 5, 2017 • Reply