Missing Series

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Hi Guys,

Hope you liked our last post on different approaches to calculate averages, today we will be discussing about missing series. A very clear instruction- To be proficient in solving series you have to practice a lot because series can be made by using any of the mathematical operation known so you need to practice as much type of questions as you can. But today we will discuss certain questions that are frequently asked in exams also I will provide you with some tips which will help you determine the missing number in series.

Let us take a question:

A.   9   11   16   26   ?   69.    

How do i solve this ? Look at the series above. Numbers are increasing from left to right so suddenly only two things comes in mind either they are getting added by certain number or multiplied. Now, which one of the two should I choose ‘multiplication or addition’. Just look at the series again, all the numbers are very close to each other there is no such two numbers which has a big difference so this strictly tells us that addition must be going on between them. Let us see.

9+2=11
11+5=16
16+10=26
26+17=43
43+26=69

So. basically an addition of 2 , 5 , 10, 17 , 26 took place where each of these numbers had a difference of 3 , 5 , 7 , 9 . (Common difference of 2).

So, the missing number was 43

Look at this series:

B.  3   4   10   33   136   ?

In this case you can see that 33 is preceded by 10 and immediately followed by 136 which simply says that this must be a case of multiplication, you cannot obtain 136 by adding certain number to 33 if you have obtained 33 by adding certain number to 10. so this is only possible in case you are multiplying. Let us see:

3*1 + 1 = 4
4*2 + 2 = 10
10*3 + 3= 33
33*4 + 4 = 136

You have the series now, thus the missing number would be 136*5 + 5 = 685

C.  6   3    3    6    24    ?

What could be the answer in this case ? here we have a decreasing – increasing series of numbers. But can you notice one thing- 6 is followed by 3 and how can you get that ?

Either you do 6-3=3 but no, I can see that series increases further so subtraction will not work or you divide 6/2=3 but again you can see that 24 is preceded by 6 which means there must be multiplication going on.

But did you notice one thing in above line I wrote 6/2=3 , which also means 6*0.5=3 . Let us see if this works.

6*0.5=3
3*1=3
3*2=6
6*4=24
24*8=192

So the numbers were getting multiplied by 0.5, 1, 2,  4,  8 and each of them are getting multiplied by (*2).

Let us take another case :

D.  3   4   12   16    48    ?

Can you identify which type of series is this ? look at the numbers.

3*4=12
4*4=16
12*4=48
16*4=64

Did you notice there was a relation between alternate numbers and the mathematical operation used was multiplication (*4). Such series are known as Alternate series. 

Try this out :

E.  2   3    4    9    8    27   ?

2*2=4
3*3=9
4*2=8
9*3=27
8*2=16

Did you notice? Here the consecutive elements of series don’t have relations, but the alternate elements have a relation.

2-4-8- these elements have a relationship- they are elements of table of 2.

3-9-27- these elements have relationship- they are elements of table of 3.

This was also an alternate series but here the multiplying factor wasn’t common unlike the previous questions.You will have to keep a check as your multiplying factors may also appear in series.

So these were certain tips that you can keep in mind while solving missing series and I am sure this will save your time and help you obtain missing numbers.

It’s Practice time, Try yourself :

1) 5, 25, 7,______, 9, 19

a) 23
b) 22
c) 25
d) 32
e) None of The Above

 2) 62, 64,______, 32, 14,16

a) 26
b) 28
c) 30
d) 32
e) None of The Above

3) 100, 50, 52, 26, 28,______

a) 30
b) 32
c) 14
d) 16
e) None of The Above

4) 980, 392, 156.8,______, 25.088, 10.0352

a) 62.72
b) 63.85
c) 65.04
d) 60.28
e) None of The Above

5)113, 225, 449,_____, 1793

a) 789
b) 786
c) 897
d) 987
e) None of The Above

Answers:

  1. Solution (Option B)
  2. Solution (Option C)
  3. Solution (Option C)
  4. Solution (Option A)
  5. Solution (Option C)

Were you able to get all your answers correct ? Here are few points that will help you approach to an unknown question.

  1. When ever you find a series, look for relations between two numbers, you can find relations between consecutive numbers, alternate numbers, or numbers at a gap of two, three etc.
  2. Once you identify these two numbers, try to recognize which mathematical operation has been done between the two, above mentioned examples will help you find the trick to do so.
  3. Just follow the series to reach out to your answer.

 

(Written by Yeshu)

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