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

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Is the number of members of Club X greater than the number [#permalink] New post 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
[Reveal] Spoiler: OA
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Re: clubX [#permalink] New post 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.

Answer: C.


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 o [#permalink] New post 08 May 2012, 05:35
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From what I can deduce, we can make a table for the two possibilities (table formatting is a mess, sorry) :

...................|.Club Y..........NOT Club Y |
Club X...........|....? ..............................| X
NOT Club X.....|.....................................|
.......................Y
Let X be the number of members in club X and let Y be the number of members in club Y. Question stem asks whether X>Y?

1. Top left corner contains info about number common number of members in both clubs. Thus, ? = .2 X But we can't decide whether X>Y. NOT SUFFICIENT.

2. Top left corner contains info about number common number of members in both clubs. Thus, ? = .3 Y But we can't decide whether X>Y. NOT SUFFICIENT.

Combine the two, ? = .2X = .3 Y. Since number of members is a positive integer, we know the answer to X>Y. SUFFICIENT.

Answer C.
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Is the number of members of Club X greater than the number [#permalink] New post 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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Is the number of members of Club X greater than the number of me [#permalink] New post 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
=> X>Y Answer C
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Re: Is the number of members of Club X greater than the number o [#permalink] New post 03 Dec 2013, 21:31
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
=> X>Y Answer C


yes, i agree with your approach. It was very hard for me to understand how can we equate 0.2x = 0.3y. I do not seem to get the correlation between these 2 statements to equate 0.2Y = 0.3 Y.

Thanks!
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Re: Is the number of members of Club X greater than the number [#permalink] New post 02 Jul 2014, 14:44
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: :-D :) :( :o :shock: :? 8-) :lol: :roll: :wink:
Group Y: :-D :) :( :o :shock: :? 8-) :lol: :x :P :oops: :cry:

So what makes up group x's overlap?

:-D :) :( :o :shock: :? 8-) :lol:

What makes up group y's overlap?

:-D :) :( :o :shock: :? 8-) :lol:

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 [#permalink] New post 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.

Answer: C.


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 [#permalink] New post 30 Jul 2014, 08:03
Expert's post
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.

Answer: C.


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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is the number of members of Club X greater than the number   [#permalink] 30 Jul 2014, 08:03
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