GATE Questions

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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.

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.

'Internet' is the shortened form of 'INTERnational-NETwork' which is the interconnected network of all the Web Servers worldwide. It is often called the 'World Wide Web'. 

The given number series is 8, 14, 24, 40, ? .

It follows a pattern that,

8

8 x 1.5 + 2 = 14

14 x 1.5 + 3 = 24

24 x 1.5 + 4 = 40

40 x 1.5 + 5 = 65

Hence, the next number in the given number series is 65.

There are 16 small cubes attached to the outer walls of the cuboid.
Therefore remaining inner small cubes will be the cubes having two sides green coloured.
So the required number = 24 - 16 = 8

The given number series is 96, 95, 87, 78, ? 

It follows a pattern that,

$$\begin{gathered} 96 \\ 96 - 12 = 95 \\ 95 - 23 = 95 - 8 = 87 \\ 87 - 32 = 87 - 9 = 78 \\ 78 - 43 = 78 - 64 = 14 \end{gathered}$$

Hence, the next number in the given number series is 14.

The given number series is 50, 51, 47, 56, 40, ?

$$\begin{gathered} 50 \\ 50 + 12 = 51 \\ 51 - 22 = 47 \\ 47 + 32 = 56 \\ 56 - 42 = 40 \\ 40 + 52 = 65 \end{gathered}$$

Hence, the next number in the given number series is 65.

The given number series 9, 19, 21, 43, 45, ... follows a pattern that

ALternately (x 2 + 1) and  (x 1 + 2)

9 

9 x 2 + 1 = 19

19 x 1 + 2 = 21

21 x 2 + 1 = 43

43 x 1 + 2 = 45

45 x 2 + 1 = 91

Hence, the next number in the given sequence is 91.