CAT Questions

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Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.

Therefore,  Man's rate against the current = (12.5 - 2.5) = 10 km/hr.

3, 7, 6, 5, 9, 3, 12, 1, 15, ... has two different series

1) 3, 6, 9, 12, 15.....

2) 7, 5, 3, 1, .....

-1 is the next number.

Commission up to 10000 = 10000x9100 = 900 

Again after 10000, 

              Commission    :   Bonus 

                           9       :   3 

                         3x        :   x

 Therefore,   Bonus = 1380-900×14 = Rs. 120

The given number series is 90 72 56 42 36 20

9 x 10 = 90

8 x 9 = 72

7 x 8 = 56

6 x 7 = 42

5 x 6 = 30 (not 36) 

4 x 5 = 20

Hence, the odd man in the given number series is 36.

Here the given number series is 270, 261, 279, 252, 289, 243

270 - 9 = 261

261 + 18 = 279

279 - 27 = 252

252 + 36 = 288 (not equals to 289)

288 - 45 = 243

Hence, the odd number in the given number series is 289.

Here the given number series is 0, 3, 8, 15, 24, ?

The next number in the given series can be found such a way that the number series follows a pattern,

$$\begin{gathered} 22 - 4 = 0 \\ 32 - 6 = 3 \\ 42 - 8 = 8 \\ 52 - 10 = 15 \\ 62 - 12 = 24 \\ 72 - 14 = 35 \\ Hence, the next number in the iven series is 35. \end{gathered}$$

Lethargic means "sluggish", kind of inactive

Vital means full of energy, lively

So, they are antonyms.

So, for the 2nd part of the analogy, you are looking for a antonym to trite

Trite means lacking originality or freshness. Overused. Kind of like a cliche

So, an antonym could be original, unique, innovative.