GATE Questions

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The given number series is  21 56 102 160 231 316

21      56       102        160      231       316         416

   +35    +46       +58       +71      +85       +100

        +11      +12       +13      +14      +15

Hence, the next number in the given number series is 316 + 100 = 416.

The series follows a pattern that,

-9², +8², -7², +6², -5²

Here the relation in the given words is, First is the process of formation of the second.

That is, when anything melts, it forms liquid. Similarly, when anything freezes it forms solid.

Hence, Melt : Liquid :: Freeze : Solid.

Here the given series 222, 271, 308, 332, 348, 357 follows a pattern that

222

222 + 49  271

271 + 36 = 307 (NOT 308)

307 + 25 = 332

332 + 16 = 348

348 + 9 = 357

Hence, the odd man in the fiven number series is 308.

Here the first two words are synonyms. Similarly, Eyrie means a large nest. So, the synonym of Eyrie is nest.

Hence, Convent : Cloister :: Eyrie : Nest.

The pattern of given series is :

5

14 = (5x3) - 1

45 = (14x3) + 3

130 = (45x3) - 5

(?) = (130x3) + 7

=> (?) = 397

1182 = (397x3) - 9

Thus, the missing number is 397.

The given series follows a pattern that,

$$\begin{gathered} 4 + 32 = 4 + 9 = 13 \\ 13 + 52 = 13 + 25 = 38 \\ 38 + 72 = 38 + 49 = 87 \\ 87 + 92 = 87 + 81 = 198 \end{gathered}$$ 

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

The given series is 1/2, 1, 3/2, 6, 5/2, 3

1/2

1/2 + 1/2 = 1

1 + 1/2 = 3/2

3/2 + 1/2 = 2 (Not 6)

2 + 1/2 = 5/2

5/2 + 1/2 = 3

Hence, the odd man in the given number series is 6.