Aptitude Overflow
0 votes
34 views

CAT2015-79

If $x^{2}+y^{2}= 0.1$ and $\left | x-y \right |=0.2$, then $\left | x \right |+\left | y \right |$ is equal to

  1. $0.3$
  2. $0.4$
  3. $0.2$
  4. $0.6$
in Quantitative Aptitude by (11.3k points) 167 551 1327
recategorized by | 34 views

1 Answer

0 votes
Given that $:x^{2} + y^{2} = 0.1\rightarrow(1)$

and $\mid x-y \mid = 0.2\rightarrow(2)$

We know that $\mid x \mid = \left\{\begin{matrix} x \:;&x\geq 0 \\ -x\:; &x<0 \end{matrix}\right.$

Now, $x -y = 0.2$ and $x-y = -0.2 \rightarrow(3)$

We know that $:(x-y)^{2} = x^{2} + y^{2} - 2xy$

$\implies (0.2)^{2} = (-0.2)^{2} =  0.1 - 2xy$

$\implies 0.04 = 0.1 -2xy$

$\implies 2xy = 0.1 -0.04  = 0.06$

$\implies xy = 0.03$

$\therefore\: \mid xy \mid = \mid 0.03 \mid = 0.03$

Now, $(\mid x \mid + \mid y \mid)^{2} = \mid x \mid ^{2} + \mid y \mid ^{2} + 2\mid x \mid \mid y \mid $
$\implies (\mid x \mid + \mid y \mid)^{2} = x^{2} + y^{2} + 2 \mid xy \mid$

$\implies (\mid x \mid + \mid y \mid)^{2} = 0.1 + 2(0.03) = 0.1 + 0.06 = 0.16$

$\implies \mid x \mid + \mid y \mid = 0.4 $

So, the correct answer is $(B).$
by (3.7k points) 4 14 45

Related questions

4,628 questions
1,447 answers
528 comments
44,274 users