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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]

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05 Mar 2012, 18:06
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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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05 Mar 2012, 22:03
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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 o [#permalink]

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08 May 2012, 06:35
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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.

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

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14 Aug 2012, 03:41
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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]

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15 Jun 2013, 10:47
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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 o [#permalink]

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03 Dec 2013, 22:31
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

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]

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02 Jul 2014, 15:44
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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 [#permalink]

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30 Jul 2014, 08:07
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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Joined: 02 Sep 2009
Posts: 39723
Re: Is the number of members of Club X greater than the number [#permalink]

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30 Jul 2014, 09:03
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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.

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 [#permalink]

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21 Jan 2015, 07:27
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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Posts: 39723
Re: Is the number of members of Club X greater than the number [#permalink]

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21 Jan 2015, 08:55
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 [#permalink]

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21 Jan 2015, 14:12
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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

[Reveal] Spoiler:
C

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 25 Mar 2015 Posts: 11 Re: Is the number of members of Club X greater than the number [#permalink] ### Show Tags 20 Jul 2015, 23:12 Bunuel wrote: GGMAT760 wrote: Bunuel wrote: Is the number of members of Club X greater than the number of members of Club Y ? 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. If I adopt the method of assuming numbers, would this make sense- Statement 1: Assume X to have 100 members. therefore, 20% of 100 = 20 20 members of X also belong to Y Insuff. Statement 2: Assume Y to have 100 members. 30% of Y= 30 30 members of Y also belong to X Insuff. 1+2: We know: 1. 30% of Y belong to X; and 2. 20 members of X belong to Y Therefore 30% of (Y) = 20 from which we get a value of Y>X. Current Student Joined: 20 Jul 2015 Posts: 5 Location: Canada GMAT 1: 750 Q50 V41 GPA: 3 WE: Account Management (Consumer Products) Is the number of members of Club X greater than the number [#permalink] ### Show Tags 19 Dec 2015, 21:28 1 This post received KUDOS 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 Final Answer: [Reveal] Spoiler: C 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9279 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: Is the number of members of Club X greater than the number [#permalink] ### Show Tags 20 Dec 2015, 19:38 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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

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17 Feb 2016, 10:50
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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 [#permalink]

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03 Nov 2016, 17:14
[quote="TomB"]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.

Take an example,
Both club are having 1000 members, 200 of club X is having membership in Y- Insufficient
300 of club Y is having membership in X- Insufficient
Both together is not giving any conclusion, so the answer is E.

Please correct me if I am wrong
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Posts: 39723
Re: Is the number of members of Club X greater than the number [#permalink]

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04 Nov 2016, 08:34
sukeshap 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.

Take an example,
Both club are having 1000 members, 200 of club X is having membership in Y- Insufficient
300 of club Y is having membership in X- Insufficient
Both together is not giving any conclusion, so the answer is E.

Please correct me if I am wrong

Note that he correct answer is C, which you can check under the spoiler in the original post as well as in several posts above.
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Re: Is the number of members of Club X greater than the number [#permalink]

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04 Nov 2016, 08:53
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

Make a Venn Diagram. Statement one states that 20% of X are also in Y. Insufficient. Statement two states that 30% of Y are also in X. Insufficient.

When you combine them you can see from drawing a venn diagram that the number of people in both groups have to be the same. Since 20% of X has to equal 30% of Y, you can set Y to 100. 30% of 100 is 30 so that will be the both section. Since 30 has to equal 20% of X, just multiple 5 x 30. 150 is X 100 is y and 30 is both. X bigger.
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Re: Is the number of members of Club X greater than the number [#permalink]

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29 May 2017, 10:15
studentsensual 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.

Dear, Bunuel!
Please tell me whether my reasoning is correct?
Thanks

used the same approach but not sure whether this is correct

I guess if we also take into account that 20% of X = 30 % of Y than your reasoning is correct

but without this information we don't know whether 80% of X > 70% of Y (at least in my opinion)
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Re: Is the number of members of Club X greater than the number   [#permalink] 29 May 2017, 10:15
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