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 Post subject: GMAT Overlapping SetsPosted: Fri Aug 06, 2010 9:05 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Of the diplomats who attended a summit conference: 20 spoke French, 32 did not speak Russian and 20% of the diplomats spoke neither French nor Russian. If 10% of the diplomats spoke both French and Russian, then how many diplomats attended the conference?
A. 70
B. 96
C. 108
D. 120
E. 150

(D) Let’s define some variables to make notation easier:
T = Total number of diplomats at the conference.
F = Number who speak French.
R = Number who speak Russian.
B = Number who speak BOTH French and Russian.
N = Number who speak NEITHER French NOR Russian.
To solve this problem, we have to remember not to double count diplomats that speak both languages.

We have a very helpful formula for Set Overlap questions:
Group 1 + Group 2 + Neither – Both = Total.

In this case, our equation becomes:
F + R + NB = T.

Substituting the given information, we have:
20 + R + 0.2T – 0.1T = T.

We have to think a little bit to put the number of diplomats who speak Russian in terms of the total number of diplomats. Since 32 of the diplomats to do not speak Russian, we know that:
R = T – 32.

Now our equation becomes:
20 + T – 32 + 0.2T – 0.1T = T.

We can solve this for T:
20 + T – 32 + 0.2T – 0.1T = T
0.1T = 12
T = 120.

The correct answer is choice (D).

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 Post subject: Re: math: grouping, venn diagramPosted: Fri Aug 06, 2010 10:11 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Let us follow the steps of this solution on Venn diagram.
At the beginning we draw a regular Venn diagram:

Then we should keep in mind denotations we use:

And start marking numbers we get from question statement:

F = 20

So R = T - 32

N = 0.2T

B = 0.1T

So now we can construct an equation:

20 + T – 32 + 0.2T – 0.1T = T
T = 120

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