CAT 2000 — QA Question 40
ModulusEasy
If x2 + y2 = 0.1 and |x – y| = 0.2, then |x| + |y| is equal to
Answer & solution
Correct answer: 0.4
- A
0.3
0.4
- C
0.2
- D
0.6
Solution
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).