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

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Is the number of members of Club X greater than the number of members  [#permalink]

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05 Mar 2012, 17:06
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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]

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05 Mar 2012, 21:03
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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

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

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15 Jun 2013, 09:47
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clearly A or B were insufficient.

my process :
Total members = Members of X only (Say A) + Members of Y Only (Say B) + Members of Both
= A + B + both
Now from the statements both= either 0.2A or 0.3B
Total = A + B + 0.2A
or = A + B + 0.3B
Equating both
A + B + 0.2A= A + B +0.3B
0.2A=0.3B
A=1.5B
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Re: Is the number of members of Club X greater than the number of members  [#permalink]

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14 Aug 2012, 02:41
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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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02 Jul 2014, 14:44
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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]

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30 Jul 2014, 07:07
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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30 Jul 2014, 08:03
2
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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21 Jan 2015, 06:27
This question was frustrating to me. My answer is E because there was no mention of the amount of people in each club for instance: club A has 10 people, club B has 20 people

Overlap= 6B+2A

Club A then has 8 members
Club B has 14 members or if the numbers are different then Club A could have more leading to both being insufficient.

Is the assumption that there are both the same number of people in each club to start or is this a flaw??
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Re: Is the number of members of Club X greater than the number of members  [#permalink]

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21 Jan 2015, 07:55
CMAC5 wrote:
This question was frustrating to me. My answer is E because there was no mention of the amount of people in each club for instance: club A has 10 people, club B has 20 people

Overlap= 6B+2A

Club A then has 8 members
Club B has 14 members or if the numbers are different then Club A could have more leading to both being insufficient.

Is the assumption that there are both the same number of people in each club to start or is this a flaw??

We are asked whether the number of members of Club X is greater than the number of members of Club Y. How can we assume that there are equal number of people in X and Y?

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

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21 Jan 2015, 13:12
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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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19 Dec 2015, 20:28
1
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]

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20 Dec 2015, 18:38
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.

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

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17 Feb 2016, 09:50
2
1
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.

Dear, Bunuel!
Please tell me whether my reasoning is correct?
Thanks
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Re: Is the number of members of Club X greater than the number of members  [#permalink]

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28 Feb 2018, 18:49
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 Bunuel,
Could you share questions similar to this?

Thanks!
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Re: Is the number of members of Club X greater than the number of members  [#permalink]

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28 Feb 2018, 21:13
shivamtibrewala 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 Bunuel,
Could you share questions similar to this?

Thanks!

19. Overlapping Sets

For more:
ALL YOU NEED FOR QUANT ! ! !

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

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25 Mar 2018, 05:39
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Top Contributor
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.

LOTS OF practice questions

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

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14 Aug 2018, 22:11
nanz236 wrote:
clearly A or B were insufficient.

my process :
Total members = Members of X only (Say A) + Members of Y Only (Say B) + Members of Both
= A + B + both
Now from the statements both= either 0.2A or 0.3B
Total = A + B + 0.2A
or = A + B + 0.3B
Equating both
A + B + 0.2A= A + B +0.3B
0.2A=0.3B
A=1.5B

Hi Bunuel,
If A represent members of X only and B represent members of Y only, then wouldn't .2A mean 20 % of those who are members of X only are also members of Club Y which is not the correct inference.

Similarly .2B would be 20 % of those members who are members of Club Y only are also members of club X.

Alternate on the same lines will this solution work
Let x represent members of both Club X &Club Y, a= members of club X only, b=members of club Y only

x=0.2(a+x), x=0.3(b+x)

Method 1:
0.2(a+x)= 0.3(b+x)
then (a+x)/ (b+x)= 3/2
Then Members of club A= 1.5 Members of Club B

Method 2:
a+x+b=a+x+b
a+ .2(a+x)+b=a+.3(b+x)+b
again then on cancelling a and b
.2(a+x)=.3(b+x)
then (a+x)/ (b+x)= 3/2
Then Members of club A= 1.5 Members of Club B

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

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22 Aug 2018, 08:39
GMATPrepNow 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.

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.

LOTS OF practice questions

GMATPrepNow when we get this 0.2X = 0.3Y it is already clear that X is greater than Y, does it make sense to divide by 0.2 further ?
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Re: Is the number of members of Club X greater than the number of members  [#permalink]

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22 Aug 2018, 09:12
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dave13 wrote:
When we get this 0.2X = 0.3Y it is already clear that X is greater than Y, does it make sense to divide by 0.2 further ?

Good point; If x and y are positive, then 0.2x = 0.3y tells us that x > y (however, I'm not certain that this is readily apparent to everyone)

Cheers,
Brent
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Re: Is the number of members of Club X greater than the number of members  [#permalink]

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17 Mar 2019, 11:10
Stem:

Is X > Y ?

Statement 1:

Members of X AND Y are 20% of the total value of X. For example, if X = 100, 20 members of X also belong to Y.

BOTH = 0.2X

Since we don't know Y, this statement is INSUFFICIENT.

Statement 2:

Members of X AND Y are 30% of the total value of Y. For example, if Y = 100, 30 members of Y also belong to X.

BOTH = 0.3Y

Since we don't know X, this statement is INSUFFICIENT.

Combined:

Since BOTH = 0.2X and BOTH = 0.3Y, 0.2X and 0.3Y are equivalent.

0.2X = 0.3Y
10*(0.2X) = 10*(0.3Y)
2X = 3Y
X/Y = 3/2

The proportion indicates that there are 3 X's for every 2 Y's. Therefore, X > Y.

Since there is a definite answer, the combined statements are SUFFICIENT. Answer C.
Re: Is the number of members of Club X greater than the number of members   [#permalink] 17 Mar 2019, 11:10
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