## Model problems on number series

Below are three problems which deals with simple logics on series.

**Directions to solve:**

In each series look for the degree and directions of change between the numbers.

find the number that fits in the place of "?".

**Question 1**

275 15 55 45 ? 135 2.2 ?

[a] 11,405 [b]25,3.5 [c] 35,5.0 [d] 115,45

**Answer:**[a] 11,405

Solution:

This is an alternative division and multiplication series.

In 1st pattern/series (numbers in 1st,3rd,5th position and so on) each number is divided by 5 to get next.

i.e.,275/5 = 55 , 55/5 = 11 and 11/5=2.2.

Therefore, number at 5th postion (I question mark) = 55/5 = 11

In 2nd pattern/series (numbers in 2nd,4th,6th position and so on) each number is multiplied by 3 to get next.

i.e., 15 x 3=45, 45 x 3=135 and 135 x 3=405.

Therefore, number at 8th position (II question mark) = 135 x 3 = 405

**Question 2**

5, 18, 67, 260, ? 4102

[a]1632 [b]965 [c]1029 [d] 2398

**Answer:**[c] 1029

Solution:

Closely observing the numbers, the given series can be generalized to (4^{n})+n, where n=1,2,3...

i.e., 4^{1} + 1 = 5

4^{2} + 2 = 18

4^{3} + 3 = 67

4^{4} + 4 = 260

4^{5} + 5 = 1029 and

4^{6} + 6 = 2398.

hence the answer is 1029.

**Question 3**

2,6,12,20,30,?

a)42 b)56 c)72 d)34

**Answer:**[a] 42

Solution:

Closely observing the numbers, the given series can be generalized to n(n + 1) where n=1,2,3...

i.e.,1(2) = 2

2(3) = 6

3(4) = 12

4(5) = 20

5(6) = 30

6(7) = 42

hence the answer is 42.