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

x + a=5

Step-by-step explanation:

Let

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

Find the the value of (x + a).

Statement 1: 4 people speak two languages but do not speak Spanish.

x = 4.

x+a

Value for a is unknown.

(x + a). Insufficient.

Statement 3: One-fifth of the group speaks more than one language.

x + y + z + a

= 25/5

= 5

value of (x + a) unknown

Insufficient.

Putting (1) and (2) together

x + y + z + a = 5

x = 4 and a=1,

we have only one possible solution from

x + y + z + a = 5

x + a

= 4 + 1

= 5.

Sufficient.

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step-by-step explanation: