CAT Exam Model Paper 2 with solutions for free online practice

(c) log${}_{100}$ |x + y |=$\frac{1}{2}$ ⇒ ${100}^{\frac{1}{2}}$ = |x + y |
⇒ | x + y| = 10 ...(i)
Again, log${}_{10}$y − log${}_{10}$ | x| = log${}_{100}$4
log${}_{10}$y − log${}_{10}$| x| = log${}_{10}$2
$\Rightarrow {\log }_{10}\frac{\mathrm{y}}{\left|\mathrm{x}\right|}={\log }_{10}2$
⇒y = 2| x|...(ii)
From eq. (ii) we can conclude that y is always positive.
Now, when x > 0 and y > 0 (always)
| x + y| = 10
⇒ | x + 2| x|| = 10
⇒ x + 2| x| = 10 ( ∵ x > 0)
⇒ x + 2 x = 10 ⇒ x = $\frac{10}{3}$
∵y$=\frac{20}{3}$
Again, x < 0 and y > 0 (always positive)
| − x + 2| − x|| = 10
⇒ | − x + 2 x| = 10
⇒ | x| = 10
⇒ x = − 10 (∵ x < 0)∴ y= 20
Hence, x = − 10, y = 20 and x = $\frac{10}{3}$ and y = $\frac{20}{3}$