GATE Questions

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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.

All locks are bangles + All bangles are cars = A + A = A
= All locks are cars => Some cars are locks.
Hence conclusion (a) follows.
All keys are locks + All locks are bangles = A + A = A
= All keys are bangles => some bangles are keys.
Hence conclusion (b) follows.
All keys are bangles + All bangles are cars = A + A = A
= All keys are cars => Some cars are keys.
Hence conclusion (C) follows.

Thus all a, b and c follows.

The given number series is 3, 5, 13, 43, 167

3

3 x 1 + 2 = 5

5 x 2 + 3 = 13

13 x 3 + 4 = 43

43 x 4 + 5 = 177 (not equal to 167)

Hence, the odd number in the given number sequence is 167. 

The given number series is 14, 27, 105, 525, 4993

14

14 x 2 - 1 = 27

27 x 4 - 3 = 105

105 x 6 - 5 = 625 (not 525)

625 x 8 - 7 = 4993

Hence, the odd man or number in the given number series is 525.

Given number series is 61, 66, 83, 121, 185

Here the given series follows a pattern that,

$$\begin{gathered} 61 \\ 61 + 22 + 1 = 66 \\ 66 + 42 + 1 = 83 \\ 83 + 62 + 1 = 120 (not 121) \\ 120 + 82 + 1 = 185 \end{gathered}$$

Hence, the odd man in the given series is 121.

The letters move 2, 2, 3, 3, 4, 4, ... steps forward.

All baseball caps have brims, since baseball caps are hats (Fact 3) and all hats have brims (Fact 1). This rules out statement III—but it doesn’t follow that all caps, a category that may include caps that are not baseball caps, have brims (statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black.

The given number series is 35, 36, 55, 111, ?

35

35 x 1 + 1 = 36

36 x 1.5 + 1 = 55

55 x 2 + 1 = 111

111 x 2.5 + 1 = 278.5

Hence, the next number in the given number series is 278.5.