Can somebody explain the solution please.

kguo wrote:Is the number of members of Club X greater than the number of members of Club Y?

(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.


I kind of understand the explanation in the book... but I just don't understand how I would realize that I needed to do certain equation manipulations to solve the problem. Can someone explain to me how to solve this problem in layman terms?

Hi!

While you certainly can solve by manipulating equations, you can also solve with common sense and logic - very powerful tools on the GMAT that people often overlook.

We should be able to dismiss each statement by itself fairly quickly, since they each give us one relationship that's not good enough to decide which club is bigger. So, let's jump directly to combining them (if you have questions about them individually, just ask!).

From (1), we know that 20% of X belong to club Y; from (2), we know that 30% of Y belong to club X.

Here's the key - each statement is telling us how many people are members of both clubs; in other words, they're each describing the same thing.

So, we know that 20% of Y is the same as 30% of X.

Now we can use either math or logic!

Math:
20%(Y) = 30%(X)
Y/X = 30%/20%
Y/X = 3/2
Y = (3/2)X
Since we know that Y and X are both positive (you can't have negative members of a club!), we can now clearly see that Y is greater than X.

Logic:
20% of Y is 30% of X.
Well, a smaller % of Y is the same as a bigger % of X; the only way a smaller % of a number can be the same as a bigger % of another number is if the first quantity is bigger than the second! Accordingly, Y must be bigger than X.

I hope that helps!

Stuart

Stuart Kovinsky wrote:

kguo wrote:Is the number of members of Club X greater than the number of members of Club Y?

(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.


I kind of understand the explanation in the book... but I just don't understand how I would realize that I needed to do certain equation manipulations to solve the problem. Can someone explain to me how to solve this problem in layman terms?

Hi!

While you certainly can solve by manipulating equations, you can also solve with common sense and logic - very powerful tools on the GMAT that people often overlook.

We should be able to dismiss each statement by itself fairly quickly, since they each give us one relationship that's not good enough to decide which club is bigger. So, let's jump directly to combining them (if you have questions about them individually, just ask!).

From (1), we know that 20% of X belong to club Y; from (2), we know that 30% of Y belong to club X.

Here's the key - each statement is telling us how many people are members of both clubs; in other words, they're each describing the same thing.

So, we know that 20% of Y is the same as 30% of X.

Now we can use either math or logic!

Math:
20%(Y) = 30%(X)
Y/X = 30%/20%
Y/X = 3/2
Y = (3/2)X
Since we know that Y and X are both positive (you can't have negative members of a club!), we can now clearly see that Y is greater than X.

Logic:
20% of Y is 30% of X.
Well, a smaller % of Y is the same as a bigger % of X; the only way a smaller % of a number can be the same as a bigger % of another number is if the first quantity is bigger than the second! Accordingly, Y must be bigger than X.

I hope that helps!

Stuart

Stuart, is there some sort of takeaway that we could learn from this problem and apply to other similar problems?