GATE Questions

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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 series follows the pattern that,

×5+5,   ×5+5,   ×5+5,   ×5+5,   ×5+5

38 x 5 + 5  = 195

195 x 5 + 5 = 980

980 x 5 + 5 = 4905

4905 x 5 + 5 = 24530

24530 x 5 + 5 = 122655

So the missing number is 980 .

The given number series is 2, 3, 7, 16, 32, ?

$$\begin{gathered} 2 \\ 2 + 12 = 3 \\ 3 + 22 = 7 \\ 7 + 32 = 16 \\ 16 + 42 = 32 \\ 32 + 52 = 57 \\ \end{gathered}$$

Hence, the next number in the given number series is 57.

Here the series follows the pattern that, product of succesive prime numbers i.e,

 2 × 3 = 6

 3 × 5 = 15

 5 × 7 = 35

 7 × 11 = 77

 11 × 13 = 143

 13 × 17 = 221

 17 × 19 = 323

So here in place of 77 the number 63 is written.

So the wrong number is 63.

The given series 

12   24   26.5   79.5   ?   330 follows a pattern that,

12 x 2 = 24

24 + 2.5 = 26.5

26.5 x 3 = 79.5

79.5 + 3 = 82.5

82.5 x 4 = 330

Hence, the missing number is 82.5

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.

Here the series follows,

194

194 - (1x1 - 1) = 194

194 - (2x2 - 1) = 191

191 - (3x3 - 1) = 183

183 - (4x4 - 1) = 168

168 - (5x5 - 1) = 144

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March. April. May. June.
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.