Data Sufficiency

BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:48 am

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.

Answer: C
Source: Official guide

One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of people, and the two characteristics are:
- member of Club X or not a member of Club X
- member of Club Y or not a member of Club Y
So, we can set up our diagram as follows:


Since we're not told any populations, let's assign some variables.
Let X = # of Club X members
Let Y = # of Club Y members
So, we now have a diagram that looks like this:


Okay, now let's solve the question...

Target question: Is X greater than Y?

Statement 1: Of the members of Club X, 20 percent are also members of Club Y.
If X people are in Club X, then the number of THESE people whose are ALSO in Club Y = 20% of X (aka 0.2X)
So, let's add this to our diagram:


Does this provide enough information to determine whether or not X is greater than Y?
No. The reason is that we have no information about the bottom-left box:


Since there are no restrictions on the bottom-left box, there are many possible ways to complete the diagram so that we get CONFLICTING answers to the target question. Here are two:
Case a:

In this case X = 10 and Y = 2, which means X is GREATER THAN Y

Case b:

In this case X = 10 and Y = 32, which means X is LESS THAN Y

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Of the members of Club Y, 30 percent are also members of Club X.
If Y people are in Club Y, then the number of THESE people whose are ALSO in Club X = 30% of Y (aka 0.3Y)
So, let's add this to our diagram:


Using logic similar to the logic we used in statement 1, we can conclude that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the information we get TWO POSSIBLE expressions for the top-left corner:

So, these two expressions must be equal.
In other words, 0.2X = 0.3Y
Divide both sides by 0.2 to get: X = (0.3/0.2)Y
Simplify to get: X = 1.5Y
Since X and Y must be positive integers, the expression X = 1.5Y tells us that X is 1.5 TIMES as big as Y
In other words, X is definitely greater than Y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:48 am

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.

Answer: C
Source: Official guide

Solution:

Question Stem Analysis:

We need to determine whether the number of members of Club X is greater than the number of members of Club Y.

Statement One Alone:

Statement one alone is not sufficient. For example, if Club X has 100 members, then 20 of its members are also in Club Y. However, Club Y could have 50 or 200 members. In the former case, Club X has more members than Club Y, and in the latter case, Club X has fewer members than Club Y.

Statement Two Alone:

Statement two alone is not sufficient. For example, if Club Y has 100 members, then 30 of its members are also in Club X. However, Club X could have 200 or 50 members. In the former case, Club X has more members than Club Y, and in the latter case, Club X has fewer members than Club Y.

Statements One and Two Together:

If we let x and y be the total number of members in Clubs X and Y, respectively, then the number of members they have in common is 0.2x (in terms of x) or 0.3y (in terms of y). Since the number of members common to both clubs must be unique, we have:

0.2x = 0.3y

2x = 3y

x = 3y/2 = 1.5y

Since x = 1.5y, x > y. Both statements together are sufficient.

Answer: C