CAT 2000 QA Question 40 · Algebra - Inequalities & Modulus

x² + y² = 0.1                          …(i)

|x – y| = 0.2

Squaring both the sides, we get,

x² + y² – 2xy = 0.04             …(ii)

From (i) and (ii),

2xy = 0.1 – 0.04 = 0.06

Thus, x and y both are positive or both are negative.

∴ 2xy = 2|x||y|= 0.06

(|x| + |y|)² = x² + y² + 2|x||y| = 0.1 + 0.06 = 0.16

|x| + |y| > 0

∴ |x| + |y| = 0.4

Hence, option (b).