## 4 Number Series Based Questions

Dear Reader,

Below are four number series based questions for your practice.

**Question 1**

In a leading engineering college in Bangalore, students started preparing for their placement tests. They have started taking things seriously and are keen about it. One of the student gave a series and wanted his friends to find the missing no. 2,1,2,4,4,5,6,7,8,8,10,11, ?

a) 10 b) 11 c) 12 c) 14

**Answer : ** a) 10

Solution :

** Note :** When you are given a series without any consistent relation between adjacent terms, you should start to look out for sub series within the series. For example, the series in question has 3 sub series. Let us discuss more about these in our solution below :

The given series is made up of the following three sub series such that 1st, 4th, 7th, 10th and 13th terms form 1st series.

2nd,5th,8th, and 11th terms form second series and

3rd,6th,9th and 12th form 3rd series.

It is seen that question mark is put in 13th number. Hence it has to fall in the I series.

**Series I :** 2,4,6,8,10 -- In this series difference is 2. Fifth number in this series is our answer which is 10..

**Series II:** 1,4,7,10 -- Here there is a difference of 3.(starting from 1 and hence – 4,7,10,13,16…etc)

**Series III:** 2,5,8, 11 -- here there is a difference of 3. (starting from 2. Hence the series will be 2,5,8,11,14,17,20 …)

**Question 2**

Mehalika and Sonali are close friends. Mehalika came across a problem and could not solve it by herself. She sought the help of Sonali.

Mehalika gave the problem as: --finding the missing number: 3,15,35,?,99, 143. Can you help Sonali ?

a) 4, b) 6, c) 84 d) 63

**Answer : ** d) 63

Solution :

The terms of the given series can be interpreted to be 2^{2} – 1, 4^{2} – 1, 6^{2} -1 and so on. Hence the missing spot would be 8^{2} -1 = 63.

**Question 3**

Kannan and Balaji had a tough fight in solving a mathematical problem on missing number. The problem was finding the missing no.in

1 3 1 9 1 81 1 ? Can you answer ahead of Kannan and Balaji ?

a) 4 b) 1 c) 6661 d) 243

**Answer : ** c) 6561

Solution :

Number 1 is continuously given as alternate number in the series. 2nd, 4th and 6th terms for a sub series : 3,9,81 where the next number should be 81 x 81 = 6561. (Series is 3 x 3 , 9 x 9 and hence next one should be 81 x 81.)

**Question 4**

Two friends started for a picnic to Mahabalipuram for sightseeing. They were watching Pallava sculptures – Seashore temple, Five rathas, Arjuna penance etc. While walking one friend posed a “Find the missing number” question to another friend. Qn. ? , 6, 30, 120, 360, 720. Can you help ?

a) 5 b) 1 c) 8 d) 3

**Answer : ** b) 1

Solution :

Third term = Second term x 5

Fourth term = Third term x 4

Fifth term = Fourth term x 3 and so on.

Therefore. Second term = first term x 6

Or 6 = first term x 6

Or first term = 1

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