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# Is the number of members of Club X greater than the number of members

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Re: Is the number of members of Club X greater than the number of members [#permalink]
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Using the table it can also be solved easily. As the individual entries result in insufficient data, options A/B/D can be eliminated.
Combining both the entries we can observe under the column "members of X and members of Y" ,the value of .2X=.3Y, which answers X>Y .Hence C is the ans.
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Re: Is the number of members of Club X greater than the number of members [#permalink]
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I got this question wrong because I didn't think to set the x and y statements against each other, because in my mind I just pictured .2x and .3y as different figures. After I reviewed the problem I pictured it this way and it became clear (I'm not using the numbers from the problem):

Group X:
Group Y:

So what makes up group x's overlap?

What makes up group y's overlap?

In my example 80% of group X is in group y, and 66.6% of group y is in group b, but the actual count is the exact same for both so you can set them against each other.
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Re: Is the number of members of Club X greater than the number of members [#permalink]
Bunuel wrote:
TomB 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.

can we use matrix approach for this question. every body is saying:
0.20x=0.30y
x/y=3/2 so x>y.

what i know is ratios are not enough to compare two quantities. I am very bad at Ratio and proportions. Please explain

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 --> 20% of X are members of both X and Y --> 0.2X={both}. Not sufficient.

(2) Of the members of Club Y, 30 percent are also members of Club X --> 30% of Y are members of both X and Y --> 0.3Y={both}. Not sufficient.

(1)+(2) 0.2X={both}=0.3Y --> X/Y=3/2 --> X>Y. Sufficient.

TomB wrote:
0.20x=0.30y
x/y=3/2 so x>y.

what i know is ratios are not enough to compare two quantities. I am very bad at Ratio and proportions. Please explain

If x and y are both negative then x<y, for example: x=-3<-2=y and if x and y are both positive then x>y. So generally you are right x/y=3/2 is NOT enough to say whether x>y. Though in our case since x and y represent # of people then we know that they must be positive integers, so case 1 is ruled out and we CAN say that x>y.

Hope it's clear.

Hi
Can I solve this kind of question by assuming total numbers??
for example while combining 1 and 2:
I assumed 100 total members then assumed two scenarios :
1: X group: 30 members: 20% in Y , 51 in X
2 Y group: 70 : 70+6 = 76 30% IN X

The same way vice versa situation where X is 70 and Y is 30:
By doing this way I got E....
cAN you pls explain why my approach is wrong???
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Re: Is the number of members of Club X greater than the number of members [#permalink]
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GGMAT760 wrote:
Bunuel wrote:
TomB 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.

can we use matrix approach for this question. every body is saying:
0.20x=0.30y
x/y=3/2 so x>y.

what i know is ratios are not enough to compare two quantities. I am very bad at Ratio and proportions. Please explain

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 --> 20% of X are members of both X and Y --> 0.2X={both}. Not sufficient.

(2) Of the members of Club Y, 30 percent are also members of Club X --> 30% of Y are members of both X and Y --> 0.3Y={both}. Not sufficient.

(1)+(2) 0.2X={both}=0.3Y --> X/Y=3/2 --> X>Y. Sufficient.

TomB wrote:
0.20x=0.30y
x/y=3/2 so x>y.

what i know is ratios are not enough to compare two quantities. I am very bad at Ratio and proportions. Please explain

If x and y are both negative then x<y, for example: x=-3<-2=y and if x and y are both positive then x>y. So generally you are right x/y=3/2 is NOT enough to say whether x>y. Though in our case since x and y represent # of people then we know that they must be positive integers, so case 1 is ruled out and we CAN say that x>y.

Hope it's clear.

Hi
Can I solve this kind of question by assuming total numbers??
for example while combining 1 and 2:
I assumed 100 total members then assumed two scenarios :
1: X group: 30 members: 20% in Y , 51 in X
2 Y group: 70 : 70+6 = 76 30% IN X

The same way vice versa situation where X is 70 and Y is 30:
By doing this way I got E....
cAN you pls explain why my approach is wrong???

Your approach does not make much sense. The statements give certain relationship between the numbers in X and Y, you cannot assume arbitrary values for them.

Also, if there are 30 members in X, then 20% of them, so 6 members, are also in Y. Now, we also know that these 6 members comprise 30% of Y, so 0.3Y=6 --> Y=20 --> X=30 > Y=20.
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Re: Is the number of members of Club X greater than the number of members [#permalink]
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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

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Re: Is the number of members of Club X greater than the number of members [#permalink]
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EMPOWERgmatRichC wrote:
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

GMAT assassins aren't born, they're made,
Rich

I'm still quite not getting it:

What if Club X had 100 people, 20 of whom are also in Club Y. But then Club Y had 50 people, 15 of whom are also in Club X.

But then you can reverse those values, and you could say what if Club x had 50 people, 10 of whom are in Club y, and Club y had 100 people, 30 of whom are in Club X.

Why does this above logic not make sense (sets the answer as E)? It must not, as the answer is C.

EDIT: nevermind, I just got it. You can't make up those 2 values as it results in the Club X+Y group having two different values, when they are 1 group. Clearly didn't follow that...I'll leave my thinking and train of thought incase it helps someone else.
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Re: Is the number of members of Club X greater than the number of members [#permalink]
Hi oseebhai,

The work that you did in your 'example' is actually really USEFUL - once you notice that the two numbers MUST be the same, you have the proof that the values of X and Y ARE related (so the answer must be C). Sometimes the work that you have to do in a DS questions helps you to prove what is NOT possible - and while it might not be the most straight-forward approach, it can still help you to still answer the question correctly.

GMAT assassins aren't born, they're made,
Rich
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TomB 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.

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

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:

Originally posted by BrentGMATPrepNow on 25 Mar 2018, 06:39.
Last edited by BrentGMATPrepNow on 01 Aug 2021, 06:34, edited 2 times in total.
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Re: Is the number of members of Club X greater than the number of members [#permalink]
TomB 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.

can we use matrix approach for this question. every body is saying:
0.20x=0.30y
x/y=3/2 so x>y.

what i know is ratios are not enough to compare two quantities. I am very bad at Ratio and proportions. Please explain

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.

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Re: Is the number of members of Club X greater than the number of members [#permalink]
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TomB 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.

can we use matrix approach for this question. every body is saying:
0.20x=0.30y
x/y=3/2 so x>y.

what i know is ratios are not enough to compare two quantities. I am very bad at Ratio and proportions. Please explain

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Re: Is the number of members of Club X greater than the number of members [#permalink]
GMAT Data Sufficiency - Is X or Y larger? Can we use a third element?

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Video solution from Quant Reasoning:
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