Data Sufficiency

BTGmoderatorDC wrote:In a group of 25 people, only three languages are spoken - English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German?

(1) 4 people speak two languages but do not speak Spanish
(2) One fifth of the group speaks more than one language.

OA C

Source: Veritas Prep

Say,

the number of people who speak only English = E;
the number of people who speak only German = G;
the number of people who speak only Spanish = S;

the number of people who speak only English & German but not Spanish = x;
the number of people who speak only English & Spanish but not German = y;
the number of people who speak only German & Spanish but not English = z;

the number of people who speak only German & Spanish & English = a ≥ 1 (given)

We have to get the value of (x + a).

Let's take each statement one by one.

(1) 4 people speak two languages but do not speak Spanish.

=> x = 4. We do not know that value for a. Can't get the value of (x + a). Insufficient.

(2) One-fifth of the group speaks more than one language.

=> x + y + z + a = 25/5 = 5

Can't get the value of (x + a). Insufficient.

(1) and (2) together

Since x + y + z + a = 5 and x = 4 and a ≥ 1, we have only one possible solution from x + y + z + a = 5 and that is a = 1. YThus, x + a = 4 + 1 = 5. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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