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

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Joined: 02 Nov 2017
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Re: Is the number of members of Club X greater than the number  [#permalink]

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28 Feb 2018, 19:49
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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Joined: 02 Sep 2009
Posts: 55188
Re: Is the number of members of Club X greater than the number  [#permalink]

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28 Feb 2018, 22:13
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  [#permalink]

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02 Mar 2018, 23:25
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!

i tried to explain you through table. Hope you understand.
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Joined: 12 Sep 2015
Posts: 3717
Is the number of members of Club X greater than the number  [#permalink]

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25 Mar 2018, 06:39
1
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  [#permalink]

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14 Aug 2018, 23:11
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

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

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22 Aug 2018, 09:35
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

Statement One: Of the members of Club X, 20 percent are also members of Club Y. Hence X - 0.20X = Both X and Y

Statement Two: Of the members of Club Y, 30 percent are also members of Club X. Hence Y - 0.30y = Both X and Y

combining both STs:

This implies that 20% of X equals 30% Y --- > 0.20X =0.30y which means that number of members in Club X is greater than that in club Y

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

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22 Aug 2018, 09:39
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  [#permalink]

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22 Aug 2018, 10:12
1
Top Contributor
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  [#permalink]

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17 Mar 2019, 12:10
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   [#permalink] 17 Mar 2019, 12:10

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