QUESTION

CSAT

Easy

Reasoning

Prelims 2015

In a group of persons traveling in a bus, 6 persons can speak Tamil, 15 can speak Hindi, and 6 can speak Gujarati. In that group, none can speak any other language. If 2 persons in the group can speak two languages only, and one person can speak all three languages, then how many persons are there in the group?

Select an option to attempt

Explanation

Let $x$ and $y$ be real numbers such that $(x+y)^2 = 16$ and $xy = 3$ . Then $x^2 + y^2$ is equal to

(a) $10$ (b) $7$ (c) $4$ (d) $19$

Solution:

We are given that $(x+y)^2 = 16$ and $xy = 3$ . We know that $(x+y)^2 = x^2 + 2xy + y^2$ . Substituting the given values, we have $16 = x^2 + 2(3) + y^2$ . $16 = x^2 + 6 + y^2$ . Therefore, $x^2 + y^2 = 16 - 6 = 10$ . The value of $x^2 + y^2$ is $10$ .