CAT Exam Model Paper 2 with solutions for free online practice

(c) log‌100 |x + y |=

1

2

⇒ 100

1

2

= |x + y |
⇒ | x + y| = 10 ...(i)
Again, log‌10y − log‌10 | x| = log‌1004
log‌10y − log‌10| x| = log‌102
⇒log10

y

|x|

=log102
⇒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 =

10

3

∵y=

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 =

10

3

and y =

20

3