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# Number Series Tricks & Tips

What is Number Series?

Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers.

In competitive exams number series are given and where you need to find missing numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can .

Generally, two kinds of series are asked in the examination.  One is based on numbers and the other based on alphabets.

Step 1: Observer are there any familier numbers in the given series.  Familier numbers are primes numbers, perfect squares, cubes … which are easy to identify.
Step 2: Calculate the differences between the numbers.  Observe the pattern in the differences.  If the differences are growing rapidly it might be a square series, cube series, or multiplicative series.  If the numbers are growing slowly it is an addition or substration series.

If the differences are not having any pattern then
1.  It might be a double or triple series.  Here every alternate number or every 3rd number form a series
2.  It might be a sum or average series.  Here sum of two consecutive numbers gives 3rd number.  or average of first two numbers give next number

Step 3: Sometimes number will be multiplied and will be added another number So we need to check those patterns.

Different types of Number series:

1) Integer Number Sequences– There are particular formulas tricks to solve number series. Each number series question is solved in a particular manner. This series is the sequence of real numbers decimals and fractions. Number series example of this is like 1, 3, 5, 9….. etc. in which what should come next is Solved by number series shortcuts tricks performed by the candidate.

2) Rational Number Sequences– These are the numbers which can be written as a fraction or quotient where numerator and denominator both consist of integers. An example of this series is ½, ¾, 1.75 and 3.25.

3) Arithmetic Sequences – It is a mathematical sequence which consisting of a sequence in which the next term originates by adding a constant to its predecessor. It is solved by a particular formula given by the mathematics Xn = x1 + (n – 1)d. An example of this series is 3, 8, 13, 18, 23, 28, 33, 38, in which number 5 is added to its next number.

4) Geometric Sequences – It is a sequence consisting of a multiplying so as to group in which the following term starts the predecessor with a constant. The formula for this series is Xn= x1 r n-1. An example of this type of number sequence could be the following:
2, 4, 8, 16, 32, 64, 128, 256, in which multiples of 2 are there.

5) Square Numbers – These are also known as perfect squares in which an integer is the product of that integer with itself. Formula= Xn= n. An example of this type of number sequence could be the following:
1, 4, 9, 16, 25, 36, 49, 64, 81, ..

6) Cube Numbers – Same as square numbers but in these types of series an integer is the product of that integer by multiplying 3 times. Formula= Xn=n^3. Example:-1, 8, 27, 64, 125, 216, 343, 512, 729, …

7) Fibonacci Series – A sequence consisting of a sequence in which the next term originates by addition of the previous two
Formula = F0 = 0, F1 = 1
Fn = Fn-1 + Fn-2. An example of this type of number sequence could be the following:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

Important Points to remember:

i). If numbers are in ascending order in the number series.

• Numbers may be added or multipliedby certain numbers from the first number.

SET – I:

Step 1 : Check whether it is ascending , descending or mixed order.

Step 2 : It is  in ascending order. So add or multiply by certain numbers from the first number.

Step 3 : The difference between first number and second, and difference between second and third and so on., are in increasing order of +4 and +3

Step 4: Hence the answer for above series is 37.

Step 1 : Check whether it is ascending , descending or mixed order.

Step 2 : It is  in ascending order. So add or multiply by certain numbers from the first number.

Step 3 : By adding  first number and second, and  second and third and so on., it is not in the sequence of increasing order. Try multiplication

Step 4: Take 1 and 3, let’s start multiplying 1*3=3, by seeing this we get to know, by multiplying 3*4 it gives 12, and 12*5=60.

Step 4: Hence the answer for above series is 360.

ii). If numbers are in descending order in the number series,

• numbers may be subtracted or dividedby certain numbers from the first number.

SET – II :

Step 1 : Find whether the given number is in descending order.

Step 2 : It is in  descending order . So subtract or divide by certain numbers  from the first number.

Step 3: The difference between first number and second, and difference between second and third and so on, are in order of -16,-8,-4,-2

Step 4: Hence the answer for above series is 3.

Step 1 : Check whether it is ascending , descending or mixed order.

Step 2 : It is  in descending order. So subtract or divide by certain numbers from the first number.

Step 3 : By dividing  first number by 6 it gives 120.

Divide 120/ 5 =24, 24/4=6, 6/3=2, 2/2=1 .It is in decreasing order.

Step 4: Hence the answer for above series is 1.

iii). If numbers are in mixing order (increasing and decreasing) in the number series.

• Numbers may be in addition, subtraction, multiplication and division in the alternate numbers.

Step 1 : Check whether it is ascending , descending or mixed order.

Step 2 : It is  in mixing order. So it may be in addition, subtraction, division and multiplication, squares and cubes.

Step 3 : In above series it is mixing of square, addition and subtraction.

(14)2= 196+4= 200

(13)2=169. By adding 4 it gives 173. Try subtraction.

169-4=165

Here we found it is in order of squaring a number, adding by 4 and subtracting by 4.

Step 4: Hence the answer for above series is 77.

Step 1 : Check whether it is ascending , descending or mixed order.

Step 2 : It is  in ascending  order. So add or multiply by certain numbers from the first number.

Step 3 : In above series lets add first number with 3 i.e.,14+3= 17

But with second number we can’t able to add +3 and so on.

Let’s try adding first number and second number i.e. 14+17=31

Second and third, i.e. 17+31 =48 and so on

This series is in the form of miscellaneous

Step 4: Hence the answer for above series is 79

1. Pure Series
In this type of number series, the number itself obeys certain order so that the character of the series can be found out.
The number itself may be.
Perfect Square
Example :
121, 144, 169, 225 ?
Perfect Cube
Example :
6859, 5832, 4913, 4096, 3375, ?
2. Difference Series
Example :
1348, 1338, 1318, 1288, 1248, ?
3. Ratio Series
Example :
336, 168, 84, 42, 21, ?
4. Mixed Series
Example :
222, 441, 1321, 2639, 7915, ?
5. Geometric Series
Example 1. 5, 35, 245, 1715, ?
Ans. 12005
Examples 2. 43923,3993, 363, 33, ?
Ans. 3
6. Two-tier Arithmetic Series

7. Other Type
To find the odd number from the number series. In this type of series the above rules are also followed.
Some Examples ;
2, 3, 7, 22, 89, 440, 2677, 18740
Solution : ×1+1, ×2+1, ×3+1, ×4+1, ×5+1 ……..
So, 440 is replaced by 446
5, 6, 14, 40, 89, 170, 291
Solution : +12, +32, +52, +72, +92
So, 14 is replaced by 15.
445, 221, 109, 46, 25, 114, 4
Solution : -3÷2, -3÷2……..
So,46 is replaced by 53.
12, 26, 56, 116, 244, 498, 1008
Solution : ×2+2, ×2+4 ×2+6,  ……..
So, 116 is replaced by 118
8, 27, 64, 125, 217, 343
Solution : 23, 33, 43, 53,…..
So, 217 is replaced by 216

YOU MUST LEARN SQUARES OF NUMBERS UPTO 40 AND CUBES OF NUMBERS UPTO 20.
Note: In the wrong number series, the pattern of series will always be wrong immediately before and after of the wrong number.
There are uncountable numbers of series because series is an imagination. Some of the important series pattern are discussed below:

1. Based on addition and subtraction.
4,9,14,18,24,29
the difference of two successive numbers is 5 but difference of 18 and 14 is 4, difference of  24 and 18 is 6. So, wrong number is 18. Correct answer is 19.

2. Based on multiplication and division.
18,28,40.5,60.75,91.125,136.6875
Solution: Problem with this type of series is how to identify these types of series. Check the difference between successive numbers.
—-10—-12.5—-20.25—-30.375—-45.5625
we can see that the difference is half of the previous number. 10 is not the half of 18 and 12.5 is not the half of 28. So, 28 is wrong and correct number is 27.

3. Based on square and cube.
8 27 125 512 1331 2197
Solution: 23=8, 33=27, 53=125, 83=512,113=1331,133=2197
In this all are cubes of number 2,3,5,8,11,13. These numbers are prime numbers except 8 and from 2 to 11, 7 is also prime number which is missing. In place of 83, there should be 73 i.e. 343

4. Based on mix pattern.
6,11,21,40,81,161
This series could have followed two patterns.

Pattern 1: difference is –5—10—-19—–41—80. Successive difference is2 times of previous one. But 19 and 41 is not following the pattern. We can guess that something is wrong in this term if we want 20 and 40, we have to replace 40 by 41. Hence 40 is wrong.

Pattern 2:   6
6×2-1 = 11
11×2-1 = 21
21×2 -1 = 41
41×2 – 1 = 81
81×2 -1 = 161 Hence, 40 is wrong
If you go through various types of pattern of wrong number series and have practiced them. You will not have any problem in solving the series. Now, we will discuss previous year asked questions based on number series.

Example 1:  12 12 18 45 180 1080 12285
In this series also there can be two pattern.

 Pattern 1 Pattern 2 12×1 = 12 12x(1.5) = 18 18x(1.5 +1) = 45 45x(2.5+1.5) = 180 180x(4+2.5)= 1170 1170x(6.5+4) = 12285 12x(1+0) = 12 12x(1+.5) = 18 18x(1.5+1) = 45 45x (2.5+1.5) = 180 180x(4+2) = 1080 1080x(6+2.5) = 9180

So,If it follows pattern1, the wrong number in series is 1080 and if it follows pattern2, the wrong number in series is 12285. It depends on options given in exams.

Example 2: 7 5 7 17 63 ? (SBI PO Prelims 2016)
7×1 – 2 = 5
5×2 – 3 = 7
7×3 – 4 = 17
17×4 – 5 = 63
63×5 – 6 = 309

Example 3: 50…… 61 89 154 280 (SBI PO Prelims 2016)
50+(13+1) = 52
52+(23+1) = 61
61+(33+1) = 89
89+(43+1) = 154
154+(53+1) = 280

Example 4: 17, 19, 25, 37, ……,87 (SBI PO Prelims 2016)
17 + 1 x 2 = 19
19 + 2 x 3 = 25
25 + 3 x 4 = 37
37 + 4 x 5 = 57
57 + 5 x 6 = 87

Example 5: 11, 14, 19, 28, 43, ? (SBI PO Prelims 2016)
3…5…9…15…23
2…4….6…….8

Example 6: 26 144 590 1164 ? (SBI PO Prelims 2016)
26 x 6 – 12 = 144
144 x 4 + 14 = 590
590 x 2 – 16 = 1164
1164 x 1 + 18 = 1182

Example 7: 6 48 8 70 9 63 7 Find the wrong number?
So, 70 is wrong in this series

Example 8: 1,4,11,34,102,304,911
Pattern of Series is
1
1×3+1 = 4
4×3-1 = 11
11×3+1 = 34
34×3-1 = 101
101×3+1 = 304
304×3-1 = 911

Example 9: 1,2,12,146,2880,86400,3628800
1
1x1x2=2
2x2x3=12
12x3x4=144
144x4x5=2880
2880x5x6=86400
86400x6x7= 3628800

Example 10: 0,6,23,56,108,184,279
13-20 = 1-1 =0
23-2= 8-2 =6
33-2= 27-4 = 23
43-23= 64-8 = 56
53-24= 125-16 = 109
63-25= 216-32 = 184
73-26= 343-64 =279

Example 11: 813,724,635,546,457,564,279
Hundred place digit is decreasing by 1, tens place is increasing by 1 and unit place digit is also increasing by 1. But this pattern is not followed in 564. 368 should be there in place of 564.

Example 12: 0,4,19,48,100,180,294
13-12=0
23-2= 4
33-3= 18
43-42= 48
53-52=100
63-62= 180
73-72=294

Example 13: 3.2, 4.8, 2.4, 3.6, 1.6, 2.7
3.2 x 1.5 = 4.8
4.8 ÷ 2 = 2.4
2.4 × 1.5 = 3.6
3.6 ÷ 2 = 1.8
1.8 x 1.5 = 2.4

Example 14: 2, 9,24,55,117,245
2×2+5 = 9
9×2+6 = 24
24×2+7 = 55
55×2+8 = 118
118×2+9 = 245

Example 15: 109,131,209,271,341,419
112-12 = 109
132-14 = 155
152-16 = 209
172-18 = 271
192-20 = 341
212-22 = 419

Example 16: 6, 7,27, 115,513,3069
6×2-5 = 7
7×3+6 = 27
27×4-7 = 101
101×5+8 = 513
513×6-9 = 3069

Prime number Series :

Example (1) : 2,3,5,7,11,13, ………..

Answer : The given series is prime number series . The next prime number is 17.

Example (2) :2,5,11,17,23,………..41.

Answer: The prime numbers are written alternately.

Difference Series :

Example (1): 2,5,8,11,14,17,………..,23.

Answer: The difference between the numbers is 3. (17+3 = 20)

Example (2): 45,38,31,24,17,………..,3.
Answer: The difference between the numbers is 7. (17-7=10). III. Multiplication Series:

Example (1) : 2,6,18,54,162,………,1458.
Answer: The numbers are multiplied by 3 to get next number. (162×3 = 486).

Example: (2) : 3,12,48,192,…………,3072.

Answer : The numbers are multiplied by 4 to get the next number. (192×4 =768).

Division Series:
Example(1): 720, 120, 24, ………,2,1

Answer: 720/6=120, 120/5=24, 24/4=6, 6/3=2, 2/2=1.

Example (2) : 32, 48, 72, 108, ………., 243.

Answer: 2. Number x 3/2= next number. 32×3/2=48, 48×3/2=72, 72×3/2=108,108×3/2=162.

n2Series:

Example(1) : 1, 4, 9, 16, 25, ……., 49

Answer:  The series is 12, 22, 32, 42, 52, …. The next number is 62=36;

Example (2) : 0, 4, 16, 36, 64, …….. 144.

Answer :The series is 02, 22, 42, 62, etc. The next number is 102=100.

n2−1Series :

Example : 0, 3, 8, 15, 24,35, 48, ……….,

Answer : The series is 12-1, 22-1, 32-1 etc. The next number is 82-1=63.

Another logic : Difference between numbers is 3, 5, 7, 9, 11, 13 etc. The next number is (48+15=63).

n2+1 Series :

Example : 2, 5, 10, 17, 26, 37, ………., 65.

Answer : The series is 12+1, 22+1, 32+1 etc. The next number is 72+1=50.

n2+n Series (or)  n2−n Series :

Example : 2, 6, 12, 20, …………, 42.

Answer : The series is 12+1, 22+2, 32+3, 42+4 etc. The next number = 52+5=30.

Another Logic : The series is 1×2, 2×3, 3×4, 4×5, The next number is 5×6=30.

Another Logic : The series is 22-2, 32-3, 42-4, 52-5, The next number is 62-6=30.

n3 Series :

Example : 1, 8, 27, 64, 125, 216, ……… .

Answer : The series is 13, 23, 33, etc. The missing number is 73=343.

n3+n Series :
Example : 2, 9, 28, 65, 126, 217, 344, ………..

Answer : The series is 13+1, 23+1, 33+1, etc. The missing number is 83+1=513.

n3−1Series :

Example : 0, 7, 26, 63, 124, …………, 342.

Answer: The series is 13-1, 23-1, 33-1 etc The missing number is 63-1=215.

n3+n Series :

Example : 2, 10, 30, 68, 130, ………….., 350.

Answer : The series is 13+1, 23+2, 33+3 etc The missing number is 63+6=222.

n3−n Series :

Example :0, 6, 24, 60, 120, 210, …………..,

Answer : The series is 13-1, 23-2, 33-3, etc. The missing number is 73-7=336.

Another Logic : The series is 0x1x2, 1x2x3, 2x3x4, etc. The missing number is 6x7x8=336.

n3+n2 Series :

Example : 2, 12, 36, 80, 150, …………,

Answer: The series is 13+12,23+22,33+32etc. The missing number is 63+62=252

n3−n2Series:

Example: 0,4,18,48,100,……………..,

Answer :  The series is 13-12,23-22,33-32 etc. The missing number is 63-62=180

xy, x+y Series:
Example: 48,12,76,13,54,9,32,……………,
Answer :2.  4+8=12, 7+6=13, 5+4=9   .: 3+2=5.

Some steps which may be helpful to solve number series.
Step 1: Check difference
Step 2: If step 1 does not work, then check difference of difference. If it also does not work, try to find is there any multiplication or division relationship between numbers?
Step 3: If difference is sharply increasing or decreasing, then you can guess that it may be due to multiplication or division pattern of series.
Step 4: If there is more irregularity in difference, then it may be combination of above discuss steps.
Step 5: If none of the steps works, then try to use elimination method, which may help you in eliminating 2 to 3 options.

### Tricks to solve Number Series With Detailed Examples

Below are the common pattern of questions usually asked in numbers series:

### I. Fibonnaci Series

The Fibonnaci sequence is a series of numbers where a no. is found by adding up the nos. before it. Let us understand the series with the help of an example:

Example 1:

0,1,1,2,3,5,8,13,21,___.

Example 2:

20, 12, 32, 44, 76, 120,____.

There can be 2 types of pattern in addition series.

### (A) Same number Addition series

In this type of series, the difference between 2 consecutive elements is same i.e. same digit is to be added to the previous element to obtain the next element.

Example 3:

3, 6, 9, 15, 18,___.

Sol. In the given series, the difference between the two consecutive elements is same i.e 3.

In this type of series, the number added to each term is in increasing order.

### (B) Increasing order Addition series

In the given series, the difference between 2 consecutive numbers is in increasing order.

Example 4:

2, 5, 9, 14, 20, 27,____.

Sol. In the given series, the difference between 2 consecutive numbers is in increasing order i.e 3,4,5,6,7 and 8 respectively.

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### (A) Same Number Subtraction Series

In this type of series, each time the same number is subtracted from the previous element to obtain the next element.

Example 5:

52, 49, 46, 43, 40,____.

Sol. Here the difference between 2 consecutive nos. is 3.

### (B) Increasing order Subtraction Series

Example 6:

94, 90, 85, 79, 72, 64,___.

Sol. Here the difference between 2 consecutive elements is in increasing order.

### (A) Same number multiplication Series

In this series, the ratio between 2 consecutive elements is same.

Example 7:

4, 12, 36, 108, 324,____.

In the given series, previous element is multiplied by 3 to obtain the next element and therefore the ratio between 2 consecutive elements is same.

### (B) Increasing order of Multiplication Series

In this type of series, elements are multiplied in increasing order to find the next element.

Example 8:

5, 5, 7.5, 15,___.

In the given series, the ratio between 2 consecutive elements is in increasing order and elements are multiplied by the numbers in increasing order.

### (A) Same number division series

In this type, each time the previous element is divided by same digit to obtain the next element.

Example 9:

1600, 400, 100, 25,___.

Sol. In the given series, previous element is divided by 4 to get the next element.

1600/4 = 400

400/4 = 100

100/4 = 25

25 /4 = 6.25

Therefore, the correct answer = 6.25

### (B) Increasing/Decreasing order division series

Example 10:

46080, 3840, 384, 48, 8, 2,____.

Sol. In the given series, elements are divided by 12, 10, 8, 6 and 4 respectively to obtain the next elements.

### VI. Addition & Multiplication together

Example 11:

1, 3, 7, 15, 31,____.

Sol. In such a series , addition and multiplication is used together.

Example 12:

5, 6, 14, 45, 184,____.

Sol. In this series, the previous elements are multiplied respectively by numbers in increasing order & numbers in increasing order respectively added in such multiplication to obtain the next element.

### VII. Decimal Fraction

Example 13:

36, 18, 18, 27, 54,___.

Sol. In this series, following pattern is used:

### VIII. Difference of difference series

Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.

Example 14:

1, 3, 8, 19, 39, 71,_____.

Sol. The following pattern is observed in the given series

### IX. Twin series

In this type of series, odd place element males one series while the even place elements make another series.

Example 15:

3, 6, 6, 12, 9, 18,______.

Sol. In this series, following pattern is used:

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### X. Tri-series

Example 16:

2, 9, 23, 3, 8, 25, 4,_____.

Sol. Following pattern is used in the given series

### XI. Square series & Cube series

Example 17:

4, 9, 16, 25, 36, 49,____.

Sol. In the given series, the following pattern is used

22, 32, 42, 52, 62, 72, 82

Example 18:

Sol. In the given series, the following pattern is used

13,  23,  33,  43,  53, 63

### XII. Square & Cube addition

Example 19:

2, 3, 7, 16,_____.

Sol. In the given series, the following pattern is used

Example 20:

1, 2, 10, 37,____.

Sol. In the given series, the following pattern is used

### XIII. Digital Operation of Numbers

In this type of series, the digits of each number are operated in a certain way to obtain the next element of the series.

Example 21:

94, 36, 18,_____.

Sol. In the given series, the following pattern is used

9 *4 = 36

3 * 6 = 18

1 * 8 = 8

23, 26, 24, 27, 25, 28, ?In this problem, numbers are increasing and decreasing and the variations are also small, therefore both addition and subtraction operations can take place.

23+3=26
26-2=24
24+3=27
27-2=25
25+3=28
28-2=26

Difficulty level : hard

If difference between consecutive numbers do not follow any patterns , try these patterns
(there is no need to by heart all this pattern , just know how the patterns can be in the series this will make easy to guess the pattern for you)
For series a, b, c, d, e, f, the pattern will be any one of these following patterns.

TIPS:To find the pattern try this technique.
Multiply the number before last number with 2 and compare the resultant number with the last number
1. a) If the resultant number is greater than the last number then it will be the addition or subtraction of square/cube of number i.e. pattern(I).
2. b) If the resultant number is less than the last number and difference is large, then the pattern will be any of these (II) or (III) or (IV) or (V)
3. c) If the resultant number is less than the last number but difference is small it belongs to (VI).
Solving these problems will make you understand better.
Example 1: 3, 732, 1244, 1587, 1803, 1928, ?

Step 1: 1803*2 = 3606 >1928 therefore it will be pattern (I)
Step 2: Now find the difference between the two numbers consecutively

difference between 3&732 = 729 i.e. 93
difference between 732&1244 = 512 i.e.83
difference between 1244&1587 = 343 i.e. 73
difference between 1587&1803 = 216 i.e. 63
difference between 1803&1928 = 125 i.e. 53
obviously next will be addition of 43+ 1928 = 1992
Example 2: 13, 25, 61, 121, 205, ?

Step 1: 121*2>205 and variation is small , so it will follow pattern (I)

Step 2: Difference between 13 & 25 = 12

difference between 25 & 61 = 36 (12*3)
difference between 61 & 121 = 60 (12*5)
difference between 121 & 205 = 84 (12*7)

Obviously next number in series will be addition of 108(12*9) with 205 = 313

Example 3: 1, 6, 36, 240, 1960, ?
Step 1: 240*2<1960 and the variation is large too, so the pattern will be either (II) or (III) or (IV) or (V)
Step 2: Now use the trial and error method but don’t apply it to whole series use it in any of the two numbers.

1*2 + 2*2 = 6

6*4+3*4=36

36*6+4*6=240

240*8 +5*8 =1960 so 1960*10+6*10=19660

Example 4: 13, 14, 30, 93, 376, 1885, ?

Step 1. 376*2<1885 and the variation is also large, so the pattern will be (II) or (III) or (IV) or (V)

Step 2. Use the trial and error method and find the pattern, it is wise to check in last two numbers.376*5=1880 adding 5 we get correct number 1885So pattern is 376*5+5=188513*1+1=1414*2+2=30Answer will be 1885*6+6=11316Example 5: 12, 35, 81, 173, 357, ?

Step 1. 173*2<357 and the variation is small so it will follow pattern (VI).

Step 2. 173*2=346 to get 357 add 11 .

Pattern is
173*2+11=357
12*2+11=35

Miscellaneous

Number series is a vast topic , there always an exception cases .)

Example : 7, 4, 5, 9, ? , 52.5, 160.5
If the numbers in the series are increasing and decreasing and a decimal numbers are in the series then you can guess decimal numbers playing in this series

7*0.5 + 0.5 = 4
4*1+1=5
5*1.5+1.5 = 9
9*2+2 = 20
20*2.5+2.5 =52.5

Example: 120 15 105 17.5 87.5 ?
120÷8 =15
15*7=105
105÷6=17.5
17.5*5=87.5
87.5÷4=21.875
Example: 3 6 21 28 55 66 ? 120
Difference between 3&6 is 3
Difference between 21&28 is 7
Difference between 55& 66 is 11
Difference between ? & 120 is 15 therefore the number is 105
• Try to observe if there are any familiar numbers in the given series.
• Familiar numbers are the numbers which which are easy to identify like primes numbers, perfect squares, cubes.
• If you are unable to find familiar number, Calculate the differences between the numbers and observe the pattern in the differences.
•   If the differences are growing slowly it might be an addition or subtraction series or If the differences are growing rapidly it might be a square series, cube series, or multiplicative series.
• If the differences also are not having any pattern then observe every alternate number (ie every 3rd number form a series) for any pattern.
• The possible cases may be like sum or the average of two consecutive numbers gives 3rd number.
• If still you do not find any pattern, it signifies that the series follows a complex pattern.
• Check for cases like multiplying the number and adding/subtracting a constant number from it to reach the pattern

# Practice Set On Number Series

Directions(1-5): Find the missing number in the following number series.

1. 20     24     33    49     74     ?
A) 115
B) 88
C) 96
D) 110
E) 123

Option D
Solution:
20 + 2^2 = 24
24 + 3^2 = 24
33 + 4^2 = 49
49 + 5^2 = 74
74 + 6^2 = 110
2. 1     ?     27    64     125
A) 8
B) 11
C) 12
D) 16
E) None of these

Option A
Solution:
1  = 1^3
? = 2^3 = 8
3 = 3^3
4 = 4^3
5 = 5^3
3. 12   14    17    13   ?   14   21    13
A) 11
B) 8
C) 10
D) 12
E) None of these

Option B
Solution:

12…..(+2)……14….(+3)…..17…..
(-4)……13……(-5)……8……(+6)……14……(+7)…..21…..(-8)…..13
+2, +3, -4, -5, +6, +7, -8
4. 5    11     ?      55      117
A) 22
B) 25
C) 33
D) 30
E) None of these

Option B
Solution:
5  * 2 + 1 = 11
11 * 2 + 3 = 25
25 * 2 + 5 = 55
55 * 2 + 7 = 117
5. 85     43    44    67.5     ?     345
A) 125
B) 140
C) 137
D) 112
E) None of these

Option C
Solution:
85 * 0.5 + 0.5 = 43
43 * 1 + 1 = 44
44 * 1.5 + 1.5 = 67.5
? = 67.5 * 2  + 2 = 137
137 * 2.5 + 2.5 = 345

Directions(6-10): In each of the following questions number series, there is a wrong number that does not follow the pattern of the series. Find the wrong number.

1. 62    87    187    420    812    1437
A) 87
B) 187
C) 420
D) 812
E) None of these

Option C
Solution:
62 + 5^2 = 62 + 25 = 87
87 + 10^2 = 87 + 100 = 187
187 + 15^2 = 187 + 225 = 412
412 + 20^2 = 412 + 400 = 812
812 + 25^2 = 812 + 625 = 1437
2. 120    137    170    222    290   375
A) 137
B) 170
C) 222
D) 290
E) 375

Option B
Solution:
120 + 1 * 17 = 137
137 + 2 *17 = 171
171 + 3 * 17 = 222
222 + 4 * 17 = 290
290 + 5 * 17 = 375
3. 550   542   537   521    496   460
A) 496
B) 521
C) 537
D) 542
E) 460

Option D
Solution:
550 – 2^2 = 546
546 – 3^2 = 537
537 – 4^2 = 521
521 – 5^2 = 496
496 – 6^2 = 460
4. 12      48     168     500    1260   2520
A) 500
B) 168
C) 48
D) 1260
E) 2520

Option A
Solution:
12 * 4 = 48
48 * 3.5 = 168
168 * 3 = 504
504 * 2.5 = 1260
1260 * 2 = 2520
5. 24   536   487    703     670    742
A) 536
B) 487
C) 670
D) 703
E)742

Option C
Solution:
24 + 8^3 = 536
536  – 7^2 = 487
487 + 6^3 = 703
703 – 5^2 = 678
678 + 4^3 = 742

Directions(1-5): In the following number series only one number is wrong. Find out the wrong number.

1. 484   240      118       57        5      11.25     3.625
A) 26.5
B) 57
C) 5
D) 3.625
E) 240

Option  C
Solution:
(484 / 2) – 2 = 240
(240/2) – 2 = 118
(118/2) – 2 = 57
(57/2) – 2 = 26.5
2. 5    7     16     57    244     1245     7506
A) 7506
B) 5
C)244
D) 7
E) 16

Option D
Solution:
5*1 + 1^2 = 6
6*2 + 2^2 = 16
16*3 + 3^2 = 57
57*4 + 4^2 = 244
244*5 + 5^2 = 1245
3. 4     2.5     3.5     6.5     15.5      41.25       126.75
A) 41.25
B) 6.5
C) 126.75
D) 4
E) 2.5

Option B
Solution:
4*0.5 + 0.5 = 2.5
2.5*1 + 1 = 3.5
3.5*1.5 +1.5 = 6.75
6.75*2 + 2 = 15.5
15.5*2.5 + 2.5  = 41.25
41.25*3 + 3 = 126.75
4. 210    209    211    186    202     77
A) 209
B) 77
C) 211
D) 186
E) 202

Option C
Solution:
210 – 1^3 = 209
209 + 2^3 = 213
213 – 3^3 = 186
186 + 4^3 = 202
202 – 5^3 = 77
5. 33       321       465       537        575      591     600
A) 465
B) 33
C) 600
D) 575
E) 591

Option D
Solution:
33 + 288 = 321
321 + 144 = 465
465 + 72 = 537
537 + 36 = 573
573 +18 = 591
591 + 9 = 600

Directions(6-10): What should  come in place of question mark in the following series.

6. 3    7     18    26    ?    53   64   96
A) 37
B) 30
C) 40
D) 35
E) 32

Option A
Solution:
3 + 4  * 2^0 = 7
7 + 11  = 18
18 + 4*(2)^1 = 26
26+ 11 = 37
37 + 4*(2)^2 = 53
53 + 11 = 64
64+ 4 *(2)^3 = 96
7. 1.7     3.2      2.7     4.2     3.7     ?     4.7      6.2
A) 3.8
B) 5.2
C) 4.4
D) 4.8
E) 5.5

Option B
Solution:
1.7    + 1.5 = 3.2
3.2  – 0.5 = 2.7
2.7 + 1.5 = 4.2
4.2 – 0.5 = 3.7
3.7 + 1.5 = 5.2
5.2 – 0.5 = 4.7
4.7 + 1.5 = 6.2
8. 6        8      10     42       ?       770     4578
A) 110
B) 150
C) 132
D) 148
E) 115

Option D
Solution:
6 * 1 + 1*2 = 8
8*2  – 2*3 = 10
10 * 3 + 3*4 = 42
42*4 – 4*5 = 148
148*5 + 5*6 = 770
770*6 – 6*7 = 4578
9. 7    13     31     85      247     ?
A) 733
B) 680
C)700
D) 650
E) 666

Option A
Solution:
7 + 6 = 13
13 + 3 *6 = 31
31 + 3 *18 = 85
85 + 3 * 54 = 247
247 + 3 * 162 = 733
10. 949   189.8     ?     22.776    11.388    6.8328
A) 39.98
B) 40.15
C) 48.53
D) 56.94
E) 55.55

Option D
Solution:
949  * 0.2 = 189.5
189.5 * 0.3 = 56.94
56.94 * 0.4 = 22.778
22.778 * 0.5 = 11.388
11.388 * 0.6 = 6.8328

Directions(1-5): What will come in place of question mark in the given number series.

1. 17 9      15     40      5       ?
A) 620
B) 650.25
C) 550.5
D) 688
E) 540.15

Option  B
Solution:
17 * 0.5 + 0.5 = 9
9 * 1.5 + 1.5 = 15
15 * 2.5 + 2.5 = 40
40 * 3.5 + 3.5 = 143.5
143.5 * 4.5 + 4.5 = 650.25
2. 2     9     25      82      335      ?
A) 1456
B) 1246
C) 1682
D) 1560
E) 1550

Option C
Solution:
2 * 1 + 7 = 9
9 * 2 + 7 = 25
25 * 3 + 7 = 82
82 * 4 + 7 = 335
335 * 5 + 7 = 1682
3. 1548      516     129     43     ?
A) 9.82
B) 11.11
C)13.25
D)10.75
E) 11.25

Option D
Solution:
1548/ 3   = 516
516/4 = 129
129/3 = 43
43/4 = 10.75
4. 41      164       2624       ?        6045696
A)94464
B) 84500
C)94502
D) 78542
E) 82456

Option B
Solution:
41  *   2^2 = 164
164  *  4^2 = 2624
2624  *  6^2 = 94464
94464  *  7^2 = 6045696
5. 4       9       29       119       599        ?
A) 2998
B) 4578
C) 3245
D) 2000
E) 3599

Option E
Solution:
4 * 2 + 1 = 9
9*3  + 2 = 29
29 * 4 + 3 = 119
119* 5 + 4 = 599
599*6 +5=3599

Directions(6-10): In the  following number series only one number is wrong. Find the wrong number.

6. 133     183     241      307     381      463     480
A) 307
B) 133
C) 480
D) 241
E) 381

Option  C
Solution:
133 + 50 = 183
183 + 58 = 241
241 + 66 = 307
307 + 74 = 381
381 + 82 = 463
463 + 90 = 553
7. 31     15      21    50    155.3      767.25
A) 767.25
B) 155.3
C) 15
D) 31
E) 50

Option B
Solution:
31 * 0.5 – 0.5 = 15
15 * 1.5 – 1.5 = 21
21 * 2.5 – 2.5 = 50
50 * 3.5 – 3.5 = 171.5
171.5  *  4.5 – 4.5 = 767.25
8. 18       119      708       3530       14136      42405
A) 14136
B) 708
C) 119
D) 3530
E) 42405

Option D
Solution:
18 * 7 – 7 = 119
119* 6 – 6 = 708
708 * 5 – 5 = 3540
3540 * 4 – 4 = 14136
14136 * 3 – 3 = 42405
9. 500     484     451      384      260      80
A) 80
B) 260
C) 451
D) 484
E) 500

Option B
Solution:
500 – 16 = 484
484 – 33(= 16 + 17) = 451
451 – 67(= 33 + 2 * 17) = 384
384 – 118(= 67 + 3 * 17)= 266
266 – 186(= 118 + 4 * 17)= 80
10. 9    10.8    18     21.6     36      64.8
A) 21.6
B) 10.8
C) 36
D) 18
E) 9

Option D
Solution:
9 + 1.8 = 10.8
10.8 + 2* 1.8 = 14.4
14.4 + 2 *3.6 = 21.6
21.6 + 2*7.2 = 36
36+ 2 * 14.4 = 64.8
Directions (1-5): In the following number series, a wrong number is given. Find out that wrong number.
Q1. 2  11  38  197  1172  8227  65806
(a) 11
(b) 38
(c) 197
(d) 1172
(e) 8227
Q2. 16  19  21  30  46  71  107
(a) 19
(b) 21
(c) 30
(d) 46
(e) 71
Q3. 7  9  16  25  41  68  107  173
(a) 107
(b) 16
(c) 41
(d) 68
(e) 25
Q4. 4  2  3.5  7.5  26.25  118.125
(a) 118.125
(b) 26.25
(c) 3.5
(d) 2
(e) 7.5
Q5. 16  4  2  1.5  1.75  1.875
(a) 1.875
(b) 1.75
(c) 1.5
(d) 2
(e) 4
Directions (6-10) : In each of the following questions a number series is given. After the series a number is given followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number, following the sequence of original series and answer the questions that follow the series.
Q6. 3  19  103  439  1381  2887
5  (a)  (b)  (c)  (d)  (e)
What will come in place of (b) ?
(a) 139
(b) 163
(c) 161
(d) 157
(e) None of these
Q7. 4  13  40  135  552  2765
2  (a)  (b)  (c)  (d)  (e)
What will come in place of (c) ?
(a) 123
(b) 133
(c) 127
(d) 131
(e) None of these
Q8. 5  12  4  10  3  8
6  (a)  (b)  (c)  (d)  (e)
What will come in place of (d) ?
(a) 3
(b) 5
(c) 4
(d) 7
(e) None of these
Q9. 3  13  37  87  191  401
1  (a)  (b)  (c)  (d)  (e)
What will come in place of (d) ?
(a) 169
(b) 161
(c) 171
(d) 159
(e) None of these
Q10. 8  4  6  15  52.5  236.25
12  (a)  (b)  (c)  (d)  (e)
What will come in place of (c) ?
(a) 23.5
(b) 16.5
(c) 22.5
(d) 22.25
(e) None of these
Directions (11-15) : What should come in place of question mark (?) in the following number series ?
Q11. 13  14  30  93  376  1885  ?
(a) 10818
(b) 10316
(c) 11316
(d) 11318
(e) None of these
Q12. 4  6  9  13.5  20.25  30.375   ?
(a) 40.25
(b) 45.5625
(c) 42.7525
(d) 48.5625
(e) None of these
Q13. 400  240  144  86.4  51.84  31.104   ?
(a) 19.2466
(b) 17.2244
(c) 16.8824
(d) 18.6624
(e) None of these
Q14. 9  4.5  4.5  6.75  13.5  33.75   ?
(a) 101.25
(b) 103.75
(c) 99.75
(d) 105.50
(e) None of these
Q15. 705  728  774  843  935  1050  ?
(a) 1190
(b) 1180
(c) 1185
(d) 1187
(e) None of these
SOLUTION:
S1. Ans.(d)
Sol. The series is based on the following pattern:
11 = 2 × 3 + 5
38 = 11 × 4 – 6
197 = 38 × 5 + 7
1172 ≠ 197 × 6 – 8
1172 is wrong and it should be replaced by 197 × 6 – 8 = 1174
S2. Ans.(a)
Sol. The series is based on the following pattern:
107 – 71 = 36
71 – 46 = 25
46 – 30 = 16
30 – 21 = 9
21 – 19 = 2≠4
19  should be replaced by 17 for which 21 – 17 = 4
S3. Ans.(d)
Sol. The series is based on the following pattern:
16 = 9 + 7
25 = 16 + 9
41 = 25 + 16
68 ≠ 41 + 25
68 should be replaced by 66.
S4. Ans.(c)
Sol. The series is based on the following pattern: ×0.5,×1.5,×2.5,×3.5,×4.5
Obviously, 3.5 Is the wrong number which should be replaced by 3.
S5. Ans.(b)
Sol. The series is based on the following pattern: ×0.25,×0.5,×0.75,×1,×1.25
Obviously, 1.75 is the wrong number which should be replaced by 1.5.
S6. Ans.(b)
Sol. The given series is based on the following pattern : ×6+1,×5+8,×4+27,×3+64,×2+125
Similarly, 5×6+1=31
31×5+8=163
Hence, 163 will come in place of (b).
S7. Ans.(a)
Sol. The given series is based on the following pattern
13 = 4 × 1 + 1 × 9
40 = 13 × 2 + 2 × 7
135 = 40 × 3 + 3 × 5
552 = 135 × 4 + 4 × 3
2765 = 552 × 5 + 5 × 1
Similarly,
(a) = 2 × l + 1 × 9 = 11
(b) = 11 × 2 + 2 × 7 = 36
(c) = 36 × 3 + 3 × 5 = 123
Hence, 123 will come in place of (c).
S8. Ans.(c)
Sol. The given series is based on the following pattern: ×2+2,÷2-2,×2+2,÷2-2………..
Hence, 4 will come in place of (d).
S9. Ans.(d)
Sol. The given series is based on the following pattern : ×2+7,×2+11,×2+13,×2+17,×2+19
(7, 11, 13, 17, 19, ….. are consecutive prime numbers)
Hence, 159 will come in place of (d).
S10. Ans.(c)
Sol. The given series is based on the following pattern : ×0.5,×1.5,×2.5…….
Hence, 22.5 will come in place of (c).
S11. Ans.(c)
Sol. The given number series is based on the following pattern :
13 × 1 + 1 = 14
14 × 2 + 2 = 30
30 × 3 + 3 = 93
93 × 4 + 4 = 376
376 × 5 + 5 = 1885
? = 1885 × 6 + 6 = 11316
Hence, number 11316 will replace the question mark.
S12. Ans.(b))
Sol. The given series is based on the following pattern :×1.5,×1.5,……..
S13. Ans.(d)
Sol. The given series is based on the following pattern : ×0.6,×0.6……..
S14. Ans.(a)
Sol. The given series is based on the following pattern : ×0.5,×1,×1.5,×2,×2.5…….
S15. Ans.(e)
Sol.
705 + 1 × 23 = 728
728 + 2 × 23 = 774
774 + 3 × 23 = 843
843 + 4 × 23 = 935
935 + 5 × 23 = 1050
? = 1050 + 6 × 23 = 1050 + 138 = 1188

Directions (Q.1-5): What will come in place of the question mark (?) in the following number series?
Q1. 1401, 1402, 705, ?, 77
(a) 243
(b) 242
(c) 244
(d) 246
(e) None of these
Q2. 10, 6, 12, 35, ?, 591.75
(a) 130
(b) 129.5
(c) 127.25
(d) 133
(e) None of these
Q3. 390, 198, ?, 54, 30, 18
(a) 102
(b) 100
(c) 98
(d) 96
(e) None of these
Q4. 10, 77, 474, ?, 9556, 28683
(a) 2275
(b) 2465
(c) 2195
(d) 2385
(e) None of these
Q5. 150, 50, 131, 67, 116, ?, 105
(a) 92
(b) 87
(c) 120
(d) 90
(e) None of these
Directions (Q.6-10): In each of these number series one number is wrong. Find out the wrong number.
Q6. 5, 6, 7.5, 9.75, 13.25, 18.4275
(a) 13.25
(b) 9.75
(c) 18.4275
(d) 7.5
(e) None of these
Q7. 13, 25, 41, 62, 85, 113
(a) 62
(b) 25
(c) 113
(d) 85
(e) None of these
Q8. 250, 55, 16, 8.2, 6.1, 6.328
(a) 6.328
(b) 55
(c) 8.2
(d) 6.1
(e) 16
Q9.  18, 54, 162, 491, 1466
(a) 18
(b) 491
(c) 1466
(d) 54
(e) 162
Q10. 7, 8, 24, 106, 361, 986
(a) 81
(b) 106
(c) 304
(d) 24
(e) None of these
Directions (Q.11-15): In each of these questions, a number series is given. Below the series one number is given followed by (a), (b), (c), (d) and (e) You have to complete this series following the same logic as in the original series and answer the question that follows.

Q11. 5, 9, 25, 91, 414, 2282.5
3 (a) (b) (c) (d) (e)
What will come in place of (c) ?
(a) 63.25
(b) 63.75
(c) 64.25
(d) 64.75
(e) None of these
Q12. 15, 9, 8, 12, 36, 170
19 (a) (b) (c) (d) (e)
What will come in place of (b) ?
(a) 18
(b) 16
(c) 22
(d) 24
(e) None of these
Q13. 7, 6, 10, 27, 104, 515
9 (a) (b) (c) (d) (e)
What will come in place of (d) ?
(a) 152
(b) 156
(c) 108
(d) 112
(e)  None of these
Q14. 6, 16, 57, 244, 1245, 7506
4 (a) (b) (c) (d) (e)
What will come in place of (d) ?
(a) 985
(b) 980
(c) 1004
(d) 1015
(e) None of these
Q15. 8, 9, 20, 63, 256, 1285
5 (a) (b) (c) (d) (e)
What will come in place of (e)
(a) 945
(b) 895
(c) 925
(d) 845
(e) None of these
Solutions

S6. Ans.(a)
Sol.
The pattern of the series is:
×1.2,×1.25,×1.3,×1.35,×1.4,×1.45……….

S7. Ans.(a)
Sol.
The pattern of series is:
+12,+16,+20,+24,+28

S8. Ans.(d)
Sol.
The series is:
÷5+5,÷5+5,÷5+5,÷5+5…….

S9. Ans.(d)
Sol.
The pattern of series is:
×3+1,×3-3,×3+5,×3-7,×3+9……

S11. Ans.(d)
Sol.
The pattern of the given series is :
5 × 1.5 + 1.5 = 7.5 + 1.5 = 9
9 × 2.5 + 2.5 = 22.5 + 2.5 = 25
25 × 3.5 + 3.5 = 87.5 + 3.5 = 91
91 × 4.5 + 4.5 = 409.5 + 4.5 = 414
Similarly,
(a)  3 × 1.5 + 1.5 = 4.5 + 1.5 = 6
(b)  6 × 2.5 + 2.5 = 15 + 2.5 = 17.5
(c)  17.5 × 3.5 + 3.5 = 61.25 + 3.5 = 64.75
S12. Ans.(b)
Sol.
The pattern of the given series is :
15 × 1 – 1 × 6 = 15 – 6 = 9
9 × 2 – 2 × 5 = 18 – 10 = 8
8 × 3 – 3 × 4 = 24 – 12 = 12
12 × 4 – 4 × 3 = 48 – 12 = 36
36 × 5 – 5 × 2 = 180 – 10 = 170
Similarly,
(a)  19 × 1 – 1 × 6 = 19 – 6 = 13
(b)  13 × 2 – 2 × 5 = 26 – 10 = 16
S13. Ans.(a)
Sol.
The pattern of the given series is :
7 × 1 – 1 = 6
6 × 2 – 2 = 10
10 × 3 – 3 = 27
27 × 4 – 4 = 104
104 × 5 – 5 = 515
Similarly,
(a)  9 × 1 – 1 = 8
(b)  8 × 2 – 2 =14
(c)  14 × 3 – 3 = 39
(d)  39 × 4 – 4 = 152
S15. Ans.(c)
Sol.
The pattern of the given series is :
8 × 1 + 1 = 9
9 × 2 + 2 = 20
20 × 3 + 3 = 63
63 × 4 + 4 = 256
Similarly,
(a)  5 × 1 + l = 6
(b)  6 × 2 + 2 = 14
(c)  14 × 3 + 3 = 45
(d)  45 × 4 + 4 = 184
(e)  184 × 5 + 5 = 925

• 4, 5, 6, 14, ?, 100.5
1. 32.5
2. 47.5
3. 67.5
4. 37.5
5. 27.5

Explanation :
4 * 1 + 1 = 5
5 * 1.5 – 1.5= 6
6 * 2 + 2 = 14
14 * 2.5 – 2.5 = 32.5
32.5 * 3 + 3 = 100.5
• 8 4 4 8 32 ?
1.354
2.384
3.294
4.234
5.256

Explanation :
8 * 0.5 = 4
4 * 1 = 4
4 * 2 = 8
8 * 4 = 32
32 * 8 = 256
• 2, 2, 7, ?, 87, 342
1.21
2.26
3.23
4.24
5.22

Explanation :
2 + 1² – 1 = 2
2 + 2² + 1= 7
7 + 4² – 1= 22
• 6, 8, 8, 22, ?, 151
1.43
2.42
3.44
4.47
5.48

Explanation :
6 * 1 + 2 = 8
8 * 1.5 – 4 = 8
8 * 2 + 6 = 22
22 * 2.5 – 8 = 47
47 * 3 + 10 = 151
• 4, ?, 14, 40, 88, 170
1.9
2.5
3.6
4.7
5.2

Explanation :
4 + 1² + 1= 6
6 + 3² – 1= 14
14 + 5² + 1= 40……..
• 6, 6, 7, ?, 91, 463
1.33
2.43
3.38
4.25
5.44

Explanation :
6*1 – 1 + 1 = 6
6*2 – 2 – 3 = 7
7*3 – 1 + 5 = 25
• 2, 5, 17, 50, 122, ?
1.252
2.258
3.257
4.225
5.242

Explanation :
2 + 1³ + 2 = 5
5 + 2³ + 4 = 17
17 + 3³ + 6 = 50
50 + 4³ + 8 = 122
• 2, 9, 39, 161, ?, 2613
1.675
2.670
3.665
4.651
5.655

Explanation :
2 * 4 + 1 = 9
9 * 4 + 3 = 39
39 * 4 + 5 = 161
161 * 4 + 7 = 651
651 * 4 + 9 = 2613
• 5, ?, 20, 34, 76, 142
1.4
2.5
3.7
4.8
5.9

Explanation :
5*2 – 2 = 8
8*2 + 4 = 20
20*2 – 6 = 34
• 5, 6, 8, 30, 136, ?
1.645
2.680
3.650
4.690
5.620

Explanation :
5 * 1 + 1 = 6
6 * 2 – 2 = 10
10 * 3 + 3 = 33
33 * 4 – 4 = 128
128 * 5 + 5 = 645

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