CAT Questions

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The given number series is 180, 90, 60, 40, 36

It follows a pattern that,

180 x 1/2 = 90

90 x 2/3  = 60

60 x 3/4  = 45 (NOT 40)

45 x 4/5  = 36

Hence, the wrong number in the given series is 40.

From statement (b)
Average of 11 players = 11 x 28 = 308
Average of 10 players = 10 x 27.3 = 273
Age of captain = 308 - 273 = 35.

From the Statement (a) we can say that captain's age (C) = y + 11 ...(1) where y-youngers age
From the statement (c),the averge age of 3groups of 3players each was given,
It means total 9 players age was given indirectly,
1st group: 25 x 3 = 75
2nd group: 28 x 3 = 84
3rd group: 30 x 3 = 90
Total  is 75 + 84 + 90 = 249
Now {C + Y + (9 players age sum)}/11 = 28
Y + 11 + Y + (249) = 28 x 11=308
2Y+260=308
2Y = 308-260 = 40 ==> Y=24 ==> C(captain's age)= Y+11 = 24+11 = 35

Therefore, statement b alone or a & c only is the answer.

The given number series 410, 409, 413, 404, ? , follows a pattern that 

410

$$\begin{gathered} 410 - 13 = 409 \\ 409 + 22 = 413 \\ 413 - 33 = 404 \\ 404 + 42 = 420 \end{gathered}$$

Hence, the next number in the given series is 420.

$$\begin{gathered} 2 = 12 + 1 \\ 3 = 22 - 1 \\ 10 = 32 + 1 \\ Now 102 - 1 = 99 \\ 9802 = 992 + 1 \end{gathered}$$

The given number series follows a pattern that

196, 169, 144, 121, 100, 81, ?

    -27  -25   -23   -21  -19  -17

=> 81 - 17 = 64

Therefore, the series is 196, 169, 144, 121, 100, 81, 64.

2.5 × 1 + 1 = 3.5

3.5 × 2 + 2 = 9

9 × 4 + 4 = 40

40 × 8 + 8 = 328

The given series is 8, 14, 24, 60, 180

8

8 x 1.5 = 12 (NOT 14)

12 x 2 = 24

24 x 2.5 = 60

60 x 3 = 180

Hence, the odd man in the given series is 12.