What percent of members take yoga classes?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun May 04, 2014 8:54 pm

Hello,

Can you please tell me where I am going wrong here. This is from Veritas practice test.

A certain health club offers only yoga classes and spin classes. If all club members take at least one type of class, what percent of members take yoga classes?

(1) 30% of members take both types of classes.

(2) 40% of members take only spin classes.

OA: B

Let total members be n. Let members taking yoga be y and spin be s

y = (?/100) (n)

1) 30/100(n) = y + s - In-suff.

2) 40/100(n) = s - In-suff.

I selected E but it's obviously wrong.

The explanation talks about using Venn diagrams.

I tried to use a double set matrix but then I still don't know the total number of members here. Can you please assist?

Thanks a lot,
Sri

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Source: Beat The GMAT — Data Sufficiency | Sun May 04, 2014 8:54 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun May 04, 2014 9:46 pm

A certain health club offers only yoga classes and spin classes. If all club members take at least one type of class, what percent of members take yoga classes?

(1) 30% of members take both types of classes.
(2) 40% of members take only spin classes.

The Double Matrix Method 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 health club members, and the two characteristics are:
- taking yoga or not taking yoga
- taking spin classes or not taking spin classes

So, we can set up our diagram as follows:

IMPORTANT: Notice that I placed a zero in the bottom right corner because we are told that all club members take at least one type of class
In other words, there are zero members who take neither yoga nor spin classes.

Also notice that I made the total population of club members = 100. This is okay since the target question asks us to find a certain PERCENT.

Target question: What percent of members take yoga classes?

In other words, we want to find the sum of the top two boxes.

Statement 1: 30% of members take both types of classes.
So, we can place 30 of the 100 members in the top-left box.

Does this provide enough information to find the sum of the top two boxes?
No.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 40% of members take only spin classes.
So, we can place a 40 in the bottom left box.

This means that a total of 40 of the 100 members do NOT take yoga.

From this, we can conclude that the remaining 60 members DO take yoga.

Brent Hanneson - Creator of GMATPrepNow.com

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun May 04, 2014 10:48 pm

Brent@GMATPrepNow wrote:
A certain health club offers only yoga classes and spin classes. If all club members take at least one type of class, what percent of members take yoga classes?

(1) 30% of members take both types of classes.
(2) 40% of members take only spin classes.

The Double Matrix Method 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 health club members, and the two characteristics are:
- taking yoga or not taking yoga
- taking spin classes or not taking spin classes

So, we can set up our diagram as follows:

IMPORTANT: Notice that I placed a zero in the bottom right corner because we are told that all club members take at least one type of class
In other words, there are zero members who take neither yoga nor spin classes.

Also notice that I made the total population of club members = 100. This is okay since the target question asks us to find a certain PERCENT.

Target question: What percent of members take yoga classes?

In other words, we want to find the sum of the top two boxes.

Statement 1: 30% of members take both types of classes.
So, we can place 30 of the 100 members in the top-left box.

Does this provide enough information to find the sum of the top two boxes?
No.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 40% of members take only spin classes.
So, we can place a 40 in the bottom left box.

This means that a total of 40 of the 100 members do NOT take yoga.

From this, we can conclude that the remaining 60 members DO take yoga.

In other words, 60% of the members take yoga.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B
-------------------------------------

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

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Cheers,
Brent

Hello Brent,

Thanks a lot for the excellent explanation.

Best Regards,
Sri

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun May 04, 2014 11:43 pm

Hi Sri,

Certain DS questions appear far more complex than they actually are.

In this DS prompt, we're told that there are 3 types of people:

1) Those who take JUST yoga classes
2) Those who take JUST spin classes
3) Those who take BOTH classes.

We're asked what percent of member take yoga classes. To answer this question, we'll need to know...
1) what percent make up groups 1 and 3
OR
2) what percent make up group 2 (then we'll know that EVERYONE ELSE takes yoga classes)

Fact 1: 30% of member take BOTH classes.

This gives us info on just group 3, which is not enough to answer the question.
Fact 1 is INSUFFICIENT

Fact 2: 40% of members take ONLY spin classes.

This tells us about group 2. By extension, everyone else MUST take a yoga class (that's 60% of members).
Fact 2 is SUFFICIENT

Final Answer: B

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

Contact Rich at [email protected]

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