Test: Series - Class 6 MCQ

The rule followed is:
(3 x 3) + (4 x 4) = 9 + 16 = 25;
(9 x 9) + (10 10) = 81 + 100 = 181
SO, (7 x 7) + (8 x 8) = 49 + 64 = 113

Correct Answer: A

Solution :

Explanation Option [a] is correct because the series follows miscellaneous pattern. Every number of the series has 2 as its 1st digit. Rest of the options is incorrect because of the correctness of option [a].

Given series: 13, 24, 46, 90, 178, ?.

24 – 13 = 11

46 – 24 = 22

90 – 46 = 44

178 – 90 = 88

The logic used here is that the difference between two successive numbers is doubled consecutively.

So, if 88 is doubled, we get 176.

Hence, 178 + 176 = 354.

Thus, the missing term in the sequence is 354.

Therefore, the complete series is 13, 24, 46, 90, 178, 354.

The given sequence is obtained as follows:

2³ – 2² = 8 – 4 = 4

3³ – 3² = 27 – 9 = 18

4³ – 4² = 64 – 16 = 48

5³ – 5² = 125 – 25 = 100

6³ – 6² = 216 – 36 = 180

7³ – 7² = 343 – 49 = 294

8³ – 8² = 512 – 64 = 448

Hence, the missing number in the series is 48.

Therefore, the complete series is 4, 18, 48, 100, 180, 294, 448.

2+3+6+9 = 20   so  20²
1+4+9+13 = 27   so  27²
9+8+11+2 = 30   so  30²

Given series: 1, 2, 10, 37, 101, ___.

1 + 1³ = 1 + 1 = 2

2 + 2³ = 2 + 8 = 10

10 + 3³ = 10 + 27 = 37

37 + 4³ = 37 + 64 = 101

101 + 5³ = 101+ 125 = 226

Thus, the given series follows a pattern of the sum of cubes of the consecutive natural numbers.

So, the complete series 1, 2, 10, 37, 101, 226.

Given series: 2, 3, 12, 37, 86, 166, 288.

2 + 1² = 2 + 1 = 3

3 + 3² = 3 + 9 = 12

12 + 5² = 12 + 25 = 37

37 + 7² = 37 + 49 = 86

86 + 9² = 86 + 81 = 167

167 + 11² = 167 + 121 = 288.

Here, the series follows a pattern of addition of the square of the consecutive odd numbers.

So, from the given number series 2, 3, 12, 37, 86, 166, 288, the wrong term is 166, because it should be 167.

Here, 5² = 25 and (5 + 1)² + 1 = 37

Similarly, 7² = 49 and (7 + 1)² + 1 = 65.

Hence, the missing number is 65.

[(6 + 3) x 3] x 2 = (9 x 3) x 2 = 27 x 2 = 54
[(7 + 2) x 7] x 2 = (9 x 7) x 2 = 63 x 2 = 126
Similarly,[ ((3 + 5) ? ] x 2 = 128
8  x ?  x  2 = 128 
128/16 = 8 

Given series: 11, 17, 39, 85, ?.

11 + (3² – 3) = 11 + 6 = 17

17 + (5² – 3) = 17 + 22 = 39

39 + (7² – 3) = 39 + 46 = 85

85 + (9² – 3) = 85 + 78 = 163

Therefore, the missing number in the given series is 163.

I.e., 11, 17, 39, 85, 163.