Fractions

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abhirup1711: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Wed Jul 13, 2011 2:27 pmFollowed by: 2 members

by abhirup1711 » Thu Jun 13, 2013 5:55 am

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3/20 members of a social club are retirees who are bridge players, 7/20 members are retirees, and one half of the members are bridge players. If 120 of the members are neither retirees nor bridge players,what is the total number of members in the social club?

240
300
360
400
480

Please help

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Source: Beat The GMAT — Problem Solving | Thu Jun 13, 2013 5:55 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

Fractions

by GMATGuruNY » Thu Jun 13, 2013 7:46 am

abhirup1711 wrote:3/20 members of a social club are retirees who are bridge players, 7/20 members are retirees, and one half of the members are bridge players. If 120 of the members are neither retirees nor bridge players,what is the total number of members in the social club?

240
300
360
400
480

Please help

This is an EITHER/OR problem.
Every member EITHER plays bridge OR doesn't.
Every member EITHER is a retiree or OR isn't.

Since the fractions in the problem are 3/20 and 7/20, let the total number of members = 20x.
To organize the data, draw a GROUP GRID:

In the grid above, B = bridge, NB = no bridge, R = retiree, NR = not a retiree.

3/20 members are retirees who are bridge players:
RB = (3/20)20x = 3x.
7/20 of the members are retirees:
R = (7/20)20x = 7x.
One half of the members are bridge players:
B = (1/2)(20x) = 10x.
Enter these values into the grid:

Complete the grid:

The grid indicates that the number of members who are neither retirees nor bridge players is equal to 6x.
Since 120 members are neither retirees nor bridge players, we get:
6x = 120
x = 20.

Thus:
Total members = 20x = 20*20 = 400.

The correct answer is D.

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Atekihcan: Master | Next Rank: 500 Posts; Posts: 149; Joined: Wed May 01, 2013 10:37 pmFollowed by: 9 members; Thanked: 54 times

by Atekihcan » Fri Jun 14, 2013 5:12 am

Total = Retirees + Players - Both + None

Say, total = N
So, retirees = 7N/20, players = N/2 = 10N/20, and both = 3N/20

So, None = total - (retirees + players - both)
So, None = N - (7N/20 + 10N/20 - 3N/20) = N - 14N/20 = 6N/20 = 3N/10

So, 3N/10 = 120
So, N = 120*10/3 = 400

Answer : D

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by Brent@GMATPrepNow » Fri Jun 14, 2013 5:21 am

I thought I'd point out that Mitch's "group grid" approach is also known as 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 social club members, and the two characteristics are:
- retirees or not retirees
- bridge players or not bridge players

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

Then try these additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

Fractions

by jain2016 » Sun Feb 07, 2016 9:02 am

Since the fractions in the problem are 3/20 and 7/20, let the total number of members = 20x.
To organize the data, draw a GROUP GRID:

In the grid above, B = bridge, NB = no bridge, R = retiree, NR = not a retiree.

3/20 members are retirees who are bridge players:
RB = (3/20)20x = 3x.
7/20 of the members are retirees:
R = (7/20)20x = 7x.
One half of the members are bridge players:
B = (1/2)(20x) = 10x.

Hi Mitch ,

One question.

R= (7/20)20x = 7x understood

It is given that 3/20 members of a social club are retirees who are bridge players , so now we have a R , which is 7x right.

So why not RB = (3/20)7x ?

Please explain and correct me.

Many thanks in advance.

SJ

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by [email protected] » Sun Feb 07, 2016 9:51 am

Hi SJ,

When dealing with Overlapping Sets questions, you have to pay careful attention to language (so that you're putting the proper 'data' in the proper 'spot').

Here, we're told that 3/20 OF MEMBERS in a club are retirees AND bridge players, so that would be (3/20)(20X).

IF.... the prompt had stated 3/20 OF RETIREES are bridge players, then the calculation would be (3/20)(7X).

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