BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OG 18 - DS- Q362 - How to solve it quickest?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Mon Sep 05, 2016 11:43 pm

OG 18 - DS- Q362 - How to solve it quickest?

by baalok88 » Sun Mar 25, 2018 1:54 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% are also members of club Y
2. Of the members of Club Y, 30% are also members of club X

The OG is explanation is too long and complex to understand. Is there a simpler method using Venn diagram?

Thanks!
Top
Source: — Quantitative Reasoning |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

OG 18 - DS- Q362 - How to solve it quickest?

by Brent@GMATPrepNow » Sun Mar 25, 2018 5:34 am
baalok88 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% are also members of club Y
2. Of the members of Club Y, 30% are also members of club X
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:
Image

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:
Image

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:
Image

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:
Image

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

Case b:
Image
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:
Image

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:
Image
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

Cheers,
Brent


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

Once you're familiar with the technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aad ... 72242.html
- https://www.beatthegmat.com/finance-maj ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability ... 73360.html
- https://www.beatthegmat.com/posted-spee ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appl ... 70255.html
- https://www.beatthegmat.com/opening-nig ... 64869.html
- https://www.beatthegmat.com/ds-french-j ... 22297.html

Difficult Problem Solving questions
- 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.beatthegmat.com/for-what-pe ... 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-peo ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume- ... 69355.html
- https://www.beatthegmat.com/mba/2011/05 ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set- ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05 ... question-3
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun Mar 25, 2018 2:37 pm
Hi All,

This DS question can be solved by TESTing VALUES.

We're asked if the number of members of Club X is greater than the number of members of Club Y? This is a YES/NO question. In these sorts of situations, it's common for some members to belong to BOTH Clubs, so we have to keep careful track of the numbers and possibilities....

Fact 1: 20% of the members of Club X are ALSO members of Club Y

IF...
Club X has 100 members, then 20 of those members ALSO belong to Club Y.
IF Club Y has 0 unique members, then the answer to the question is YES.
IF Club Y as 1,000 unique members, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: 30% of the members of Club Y are ALSO members of Club X

This Fact offers the same general logic as Fact 1 (above). Without knowing the number of unique members in Club X, the answer to the question could be either YES or NO.
Fact 2 is INSUFFICIENT

Combined, we know...
20% of the members of Club X are ALSO members of Club Y
30% of the members of Club Y are ALSO members of Club X
These specific members are the SAME PEOPLE...

This means that .2(X) = .3(Y)

2X = 3Y
X = (3/2)(Y)

This means that X MUST be greater than Y, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

Junior | Next Rank: 30 Posts
Posts: 23
Joined: Mon Mar 12, 2018 9:53 am

by Jake@ThePrincetonReview » Tue Apr 10, 2018 1:21 pm
Hi!

The absolute simplest way to solve this problem is to realize that the two statements are talking about the SAME people. That is, the people who are in both groups. So while I think it's fairly clear that neither statement individually will allow you to answer the question (but if not, other explanations here shows you why), it should be also fairly clear that because the two statements are talking about the same people that 20% of X is equal to 30% of Y, meaning that Club X has the greater number of people.


Image
Jake Schiff
GMAT Instructor and Master Trainer
Image
Curious How You'll Score? Take a FREE GMAT® practice test or sample class
Ready to Prep? Exclusive discounts for Beat The GMAT® members HERE
Top
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Tue Nov 14, 2017 2:51 pm

Here is how you want to approach

by jaetpu » Tue Jun 19, 2018 11:30 pm
baalok88 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% are also members of club Y
2. Of the members of Club Y, 30% are also members of club X

The OG is explanation is too long and complex to understand. Is there a simpler method using Venn diagram?

Thanks!

let x = members in club X
let y = members in club Y


1. Of the members of Club X, 20% are also members of club Y
â…•x. x and y are still unknown, so we don't know which is greater. Insufficient.
2. Of the members of Club Y, 30% are also members of club X
(3/10)y. Insufficient for the same reasons as 1).


if we combine 1 and 2, we can set 2/10x = 3/10y
2x=3y
x=3/2y
Thus, x>y

C
Top
Post new topic Post Reply
• Page 1 of 1