* How many Diplomats attended the conference?

[S]

Of the diplomats attending a summit conference, 20 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?

A) 72
B) 96
C) 108
D) 120
E) 150

I want to know if we can use the 2X2 matrix to solve this type of question.

I still am really confused about the use of the 2X2 table. Any help is appreciated. Thank you.

[Guest]

With this problem, using a 2x2 will NOT help.

The main point of the question is really to find out what the 10% and 20% represent. I didn't know a "textbook" way to solve this problem so I opted to plug numbers and chart it out.


French|Both|Russian|None
A) 72 20 7.2 14.4 Impossible
B) 96 20 9.6 19.2 Impossible
C) 108 20 10.8 21.6 Impossible
D) 120 20 12 24
E) 150 20 15 30

In C, since both represent 10%, it would mean there are 12 diplomats that speak both languages.
Since none represent 20%, it would mean there are 24 that speak none.

From here, we can determine that 20-12+24=32 diplomats that do not speak russian. This is enough to support our answer. The question itself states there are 32 diplomats that don't speak russian.

Choice E tells us that there are 35 (20-15+30) diplomats that do not speak russian.

Hope this helps.

[JPG]

In case you are still puzzled, I actually did use a 2X2 matrix to solve this problem. It looked something like this:


Russian No Russian Total

French: .1x y 20
No French: .7-y .2x
Total: 32 x

From the matrix I chose the two simplest equations that provided the most information:

.1x + y = 20
y + .2x = 32
.1x = 12
x = 120

Hope that helps a bit.

[S]

Thanks JPG, that was really useful.

[JonathanSchneider]

PLEASE post the source of this question, or we will be forced to delete this post.
Thanks,
Jonathan