Combined and Multi-tier Number series
Sometimes paper-setters use a couple of tricks to make the difficulty level of ‘Number series questions’ a bit higher.
Basically, they have a couple of broad tricks in their kitty:
- Combined Number series - Combination of two or more Number series
- Multi-tier Number series
Let’s study them one by one in more detail.
Combined Number series
In this type of series two or more series are mixed together, which have their own respective rules and have no relation with each other.
Generally, two series are mixed, wherein odd place elements make one series, while the even place elements make another series.
Q. Find the missing number in the following series:
2, 2, 4, 6, ?, 10, 8, 14, 10
(a) 8 (b) 6 (c) 12 (d) 10
(SSC CGL Question)
Explanation:
There are two separate number series in the given series:
- Series made by odd-position elements: 2, 4, ?, 8, 10 (difference of +2 between elements)
- Series made by even-position elements: 2, 6, 10, 14 (difference of +4 between elements)
Hence, the missing number belongs to the series made by odd-position elements.
So, missing number = 4 + 2 = 6
Answer: (b)
Q. Find the missing number in the following series:
12, 8, 14, 6, 16, ?
(a) 18 (b) 16 (c) 4 (d) 2
(SSC CGL Question)
Explanation:
There are two separate number series in the given series:
- Series made by odd-position elements: 12, 14, 16 (difference of +2 between elements)
- Series made by even-position elements: 8, 6, ? (difference of -2 between elements)
Hence, the missing number belongs to the series made by even-position elements.
So, missing number = 6 - 2 = 4
Answer: (c)
Multi-tier Number series
The differences or the differences of differences are in arithmetic progression (A.P.) or geometric progression (G.P.) with a certain common difference.
Q. Find the missing number in the following series:
2, 20, 56, 110, ?
(a) 122 (b) 182 (c) 196 (d) 172
(SSC CGL Question)
Explanation:
The given series may be represented as follows:
The differences between the numbers in the series are: 18, 36, 54, 72.
So, as we can see in the above figure, these differences are in A.P. with a common difference of 18.
Answer: (b)
Q. Find the missing number in the following series:
3, 8, 18, 35, ?, 98
(a) 55 (b) 54 (c) 61 (d) 63
(SSC CGL Question)
Explanation:
The given series may be represented as follows:
The differences of differences are in A.P. with a common difference of 2.
Answer: (c)
Q. Find the missing number in the following series:
1, 3, 8, 19, 42, ?
(a) 71 (b) 93 (c) 61 (d) 89
(SSC CGL Question)
Explanation:
The given series may be represented as follows:
The differences of differences are in G.P. with a common difference of 2.
(1 × 2) + 1 = 3
(3 × 2) + 2 = 8
(8 × 2) + 3 = 19
(19 × 2) + 4 = 42
(42 × 2) + 5 = 89
Answer: (d)