Missing Number: Meaning, Reasoning Questions, Mock Test, Examples

Missing numbers are numbers that got missed in the given series of numbers or figures with similar differences between them. In such types of questions, a figure, a set of figures, an arrangement or a matrix is given, each supporting certain terms, be it numbers, letters or a group/combination of letters/numbers, following a definite pattern. The aspirant is required to decode the pattern and accordingly find the missing term in the figure.

Types of Missing Number Reasoning Problems

1) Geometrical shape-based missing numbers
2) Matrix-based missing numbers

Approach to Solve the Missing Number Reasoning Questions

First of all, check the order of the numbers. The order of the numbers is either in ascending order or in descending order and then determine the differences between the numbers that are next to each other to calculate the missing number or we can find missing numbers by determining the pattern followed by the numbers/letters in the given series or figures. This pattern can be any of the mathematical operations such as addition, subtraction, product or combination of different operations.

Now let’s understand the types of missing number reasoning in detail -

1) Geometrical Shape-Based Missing Numbers

- In such types of questions, different geometrical shapes will be given which consist of numbers/letters inside them following a certain rule/logic or sequence. The question may contain one figure or a combination of two or more figures. You have to find the logic among the given terms to find the missing term. Some of the figures with logic are explained below.
Example:
Find the missing character from among the given alternatives.

(a) 256 (b) 289 (c) 324 (d) 196
Solution:
Here, the given numbers in the geometrical figure are the squares of consecutive odd numbers such as 112 = 121; 132 = 169; 15² = 225; 17²= 289.
Hence, the second option is correct.

Example:
Find the missing character from among the given alternatives.

(a) 1540 (b) 1440 (c)1640 (d) 1720

Solution:
Here, moving in the clockwise direction.
The pattern is as follows:
2 x 1 = 2; 2 x 2 = 4; 4 x 3 = 12; 12 x 4 = 48; 48 x 5 = 240; 240 x 6 = 1440; 1440 x 7 = 10080.

Therefore, 1440 is the required answer. Hence, the second option is correct.

Example: Triangle missing number reasoning
Find the missing character from among the given alternatives.

(a) 5 (b) 6 (c)7 (d) 8

Solution:
Here, the result of the multiplication of the outer numbers is divided by 10 to obtain the number inside the figure.

The pattern is as follows:
In the first figure: 5 x 4 x 2 = 40
40/10 = 4
In the second figure: 3 x 7 x 10 = 210
210/10 = 21
Similarly, in the third figure: 5 x 5 x 2 = 50
50/10 = 5
Therefore, the required number is 5. Hence, the first option is correct.

Example:
Find the missing character from among the given alternatives.

(a) 29 (b) 11 (c)28 (d) 13

Solution:
The pattern is as follows:
In the first figure: (8 x 5) - (4 x 3) = 40 - 12 = 28
In the second figure: (6 x 5) - (2 x 7) = 30 - 14 = 16
Similarly, In the third figure: (6 x 6) - (5 x 5) = 36 - 25 = 11

Therefore the required number is 11. Hence, the second option is correct.

Missing Number Reasoning Tricks to Solve Geometrical Shape-Based Problems

1) The first step is to identify the pattern used in the geometrical shape-based problems. There are some most common patterns such as it could be the sum of two numbers divided by a constant, being an average of numbers or being in the form of letters, where the positional values of the letters are decreased or increased etc.

2) You must know types of numbers such as whole numbers, natural numbers, prime numbers, even numbers, odd numbers etc.

3) Practice is key to success. Try to solve several missing number reasoning pdf questions by identifying the pattern, understand the pattern behind it and continue the practice.

2) Matrix-Based Missing Numbers

- In such types of questions, a matrix having rows and columns will be given which consists of numbers/letters inside them following a certain rule/logic or sequence. You have to find the logic among the given terms to find the missing term. Some of the matrixes with logic are explained below.

Example:
Find the missing character from among the given alternatives.

(a) 9 (b) 7 (c)5 (d) 12

Solution:
The pattern is as follows:
In the first column: 6 x 6 x 5 = 180
In the second column: 7 x 7 x 6 = 294
Similarly, in the third column: 8 x 8 x ? = 576
? = 576/64 = 9

Therefore, the required number is 9. Hence, the first option is correct.

Example:
Find the missing character from among the given alternatives.

(a) P (b) O (c)Q (d) R

Solution:
The letters in the second and the third rows are seven steps ahead of those in the first and second rows respectively.
The pattern is as follows:
In the second column: D(4) + 7 = K(11); K(11) + 7 = R(18)
In the third column: G(7) + 7 = N(14); N(14) + 7 = U(21)
Similarly, In the first column: A(1) + 7 = H(8); H(8) + 7 = O(15)

Therefore, the required letter is O. Hence, the second option is correct.
Example:
Find the missing character from among the given alternatives.

(a) S10 (b) U12 (c) V13 (d) R11

Solution:
The letter in each row moves two steps forward and in each row, the sum of the first two numbers is equal to the third number.
In the first row: the letters - A(1) + 3 = D(4), D(4) + 3 = G(7); the number - 3 + 6 = 9
In the second row: the letters - G(7) + 3 = J(10), J(10) + 3 = M(!3); the number - 2 + 1 = 3
Similarly, in the third row: the letters - M(13) + 3 = P(16); P(16) + 3 = S(19); the number = 4 + 6 = 10

Therefore, the required term is S10. Hence, the first option is correct.

Missing Number Reasoning Tricks to Solve Matrix-Based Problems

1. First of all, determine the numbers/letters according to rows or columns to identify the pattern.

2. Once the pattern has been identified then determine the rule that is applied to the numbers/letters it could be the BODMAS rule, squares, cubes or it could be in the form of letters, where the positional values of the letters are decreased or increased etc.

3. Practice is key to success. Try to solve several missing number reasoning practice set or missing number reasoning mcq by identifying the pattern, understand the pattern behind it and continue the practice.

4. After the solved examples there is missing number reasoning questions with answers pdf available for your reference.

Solved examples of Find the Missing Number Reasoning Questions with Answers

1) Directions: In the following question, select the missing number from the given responses.

1) 432

2) 501

3) 512

4) 332

Solution:
The numbers given in each figure are the cubes of the consecutive natural numbers.

In the first figure→(1)³ = 1; (2)³ = 8; (3)³ = 27

In the second figure→(4)³ = 64; (5)³ = 125; (6)³ = 216

In the third figure→(7)³ = 343; (8)3 = 512; (9)³ = 729

So, 512 is the missing number. Hence, the third option is correct.

2) Directions: In the following question, select the missing number from the given responses.

1) 1

2) 4

3) 9

4) 25
Solution:
The numbers given in each figure are the squares of the consecutive natural numbers.

In the first figure→(2)2 = 4; (3)2 = 9; (4)2 = 16

In the second figure→(1)2 = 1; (2)2 = 4; (3)2 = 9

In the third figure→(3)2 = 9; (4)2 = 16; (5)2 = 25

So, 25 is the missing number. Hence, the fourth option is correct.
3. Directions: In the following question, find the missing number from the given alternatives.

1) 13

2) 15

3) 17

4) 19

Solution:

Add two base numbers and divide the resultant number by 7.

In the first figure→25 + 17 = 42; 42 ÷ 7 = 6

In the second figure→38 + 18 = 56; 56 ÷ 7 = 8

In the third figure→89 + 16 = 105; 105 ÷ 7 = 15

So, 15 is the missing number. Hence, the second option is correct.

4. Directions: In the following question, find the missing number from the given alternatives.

1) 125

2) 175

3) 225

4) 250

Solution:

The number at the bottom of the figure is the square of the difference between the other two numbers given in the figure.
In the first figure→(20 – 9)² = (11)² = 121

In the second figure→(24 – 11)²= (13)2 = 169

In the third figure→(32 – 17)² = (15)² = 225

So, 225 is the missing term. Hence, the third option is correct.

5. Directions: In the following question, select the missing number from the given responses.

1) 60

2) 58

3) 65

4) 72

Solution:

To find the number at the bottom of the figure, divide the product of the other two numbers by 8.

In the first figure→(14 × 24) ÷ 8 = 336 ÷ 8 = 42

In the second figure→(64 × 12) ÷ 8 = 768 ÷ 8 = 96

In the third figure→(32 × 18) ÷ 8 = 576 ÷ 8 = 72

So, 72 is the missing term. Hence, the fourth option is correct.

6. Directions: Select the missing number from the given responses.

1) 8

2) 31

3) 32

4) 36

Solution:
The pattern can be observed running horizontally along the rows.
For each row, subtract the first number from the third number, then divide the resultant by 4 to get the second number.

First row: 26 – 6 = 20; 20 ÷ 4 = 5

Second row: 32 – 4 = 28; 28 ÷ 4 = 7

Third row: {44 – (?)} ÷ 4 = 9

⇒ 44 – (?) = 9 × 4

⇒ 44 – (?) = 36

⇒ (?) = 44 – 36

⇒ (?) = 8

So, the missing number is 8. Hence, the first option is correct.

7. Directions: In the following question, select the missing number from the given responses.

1) 6

2) 7

3) 10

4) 11

Solution:
Add the first two numbers given in the second row and divide by 2 to get the number between them in the first row.

The pattern followed is as follows –
In the first part; 16 + 20 = 36; 36 ÷ 2 = 18

In the second part; 18 + 22 = 40; 40 ÷ 2 = 20

In the third part; (9 + (?)) ÷ 2 = 8

⇒ 9 + (?) = 8 × 2

⇒ 9 + (?) = 16

⇒ (?) = 16 – 9 = 7

So, the missing number is 7. Hence, the second option is correct.

8. Directions: In the following question, select the missing number from the given responses.

1) 5

2) 2

3) 3

4) 1

Solution:
The difference in the sum of the alternate column is equal to the number given between these columns.

The pattern followed is as follows –

In the first part; 2 + 3 + 1 = 6; 4 + 3 + 2 = 9→9 – 6 = 3

In the second part; 5 + 6 + 1 = 12; 3 + 6 + 6 = 15→15 – 12 = 3

So, the missing number is 3. Hence, the third option is correct.

9. Directions: In the following question, select the missing number from the given responses.

1) 23

2) 115

3) 118

4) 220

Solution:

Here, the sum of the first four rows is multiplied by 5 which is equal to the fifth row.

Like, in the first column; (1 + 2 + 4 + 3 ) × 5 = 50

And, in the second column; (3 + 4 + 5 + 2 ) × 5 = 70

Similarly, in the third column; (7 + 4 + 9 + 3 ) × 5 = 115

So, the missing number is 115. Hence, the second option is correct.

10. Directions: In the following question, select the missing number from the given responses.

1) 11

2) 20

3) 19

4) 16

Solution:

Here, the sum of each column is equal to 40.

Like, in the first column; 13 + 11 + 16 =.40

And, in the third column; 24 + 6 + 10 = 40

Similarly, in the second column; 9 + ? + 20 = 40; ? = 11

So, the number that needs to be added is 11. Hence, the first option is correct.

For more questions you should attempt online missing number reasoning mock test and download e-book of missing number reasoning questions pdf with solution below:
Missing Number Questions with Solutions PDF

The most important verbal reasoning topics you must read:

Missing Numbers Problems for SSC MTS/ SSC CHSL/ SSC Stenographer

1) Directions: In the following question, select the missing number from the given responses.

1) 36

2) 117

3) 52

4) 26

Hint: Add and multiply the numbers on the top of the figure to get the numbers at the bottom of the figure.

Solution

For each figure, multiply and add the numbers in the top left and top right corners to get the bottom left and bottom right numbers respectively.

Figure one: 5 × 4 = 20; 5 + 4 = 9

Figure two: 3 × 8 = 24; 3 + 8 = 11

Figure three: 9 × 4 = 36; 9 + 4 = 13

Therefore, the missing number is 36. Hence, the first option is correct.

2) Directions: In the following question, select the missing number from the given responses.

1) 22

2) 24

3) 25

4) 28

Hint: Add and multiply the diagonally opposite numbers to get the other two numbers.

Solution

For each figure, multiply and add the numbers in the top right and bottom left corners to get the top left and bottom right numbers respectively.

Figure one: 4 × 7 = 28; 4 + 7 = 11

Figure two: 5 × 5 = 25; 5 + 5 = 10

Figure three: 3 × 8 = 24; 3 + 8 = 11

Therefore, the missing number is 24. Hence, the second option is correct.

3) Directions: In the following question, select the missing number from the given responses.

1) 125

2) 25

3) 625

4) 1225

Hint: For each figure, determine the fourth power of the given numbers to get the missing number.

Solution

For each figure, diagonally opposite numbers are equal to the fourth power of the number given in the top left and right corner of the square.

Like, in Figure 1: (2)4 = 16, (4)4 = 256

Figure 2: (3)4 = 81, (1)4 = 1

Similarly, in figure 3: (5)4 = 625, (4)4 = 256

Therefore, the missing number is 625. Hence, the third option is correct.

Missing Numbers Problems for SSC CPO/ SSC CGL

Directions: In the following question, a series is given with one term missing. Choose the correct alternative from the given ones that will complete the series.

1) R

2) P

3) O

4) L

Hint: Subtract 3 from the place value of the letters of each row to obtain the next letter.

Solution

Subtract 3 from the place value of the letters of each row to obtain the next letter.

Row I: K – 3 = H; H – 3 = E

Row II: B – 3 = Y; Y – 3 = V

Row III: S – 3 = P; P – 3 = M

So, P is the missing term. Hence, the second option is correct.

2) Directions: In the following question, select the missing numbers from the given responses.

1) 49, 45, 46

2) 45, 49, 46

3) 40, 48, 46

4) 46, 40, 45

Hint: Determine the missing numbers through the sum of all the numbers given in a row and a column.

Solution

Let the missing numbers in a table be X, Y, Z.

In the given table, the sum of all the numbers in a row and in a column is equal, i.e., 132.

Row 1→43 + 48 + 41 = 132

Column 1→43 + 42 + 47 = 132

Row 2→42 + 44 + X = 132

⇒ X = 132 – 44 – 42 = 46

⇒ X = 46

Column 2→48 + 44 + Y = 132

⇒ Y = 132 – 48 – 44 = 40

⇒ Y = 40

Row 3→41 + X + Z = 132

⇒ 41 + 46 + Z = 132

⇒ Z = 132 – 41 – 46 = 45

⇒ Y = 45

So, 46, 40, and 45 are the missing numbers in the given figure. Hence, the fourth option is correct.

Missing Numbers Problems for CUET/ Railway Recruitment Board exams

1) Directions: In the following question, select the missing number from the given responses.

1) 9

2) 40

3) 7

4) 36

Hint: Add the sum of the two numbers to the difference between the two numbers to get the missing number.

Solution

Here, add the sum of top and bottom numbers with the difference of left and right numbers given in the box.

Figure one: (18 + 17) + (9 – 6) = 38

Figure two: (11 + 11) + (19 – 9) = 32

Figure three: (6 + 15) + (26 – 3) = 44

Figure four: (12 + 8) + (9 – 20) = 9

Therefore, the missing term is 9. Hence the first option is correct.

2) Directions: Find out the numbers that would fit in the second-row and third-row middle and last blank spaces (?) respectively.

1) 26, 24, 25

2) 15, 21, 20

3) 21, 15, 20

4) 25, 24, 26

Hint: Check the sum of the numbers row-wise and column-wise.

Solution

Here, the sum of the numbers in a row and the sum of the numbers in a column are equal to 57.

In the first row; 18 + 23 + 16 = 57

In the second row; 17 + 19 + (?) = 57 ⇒ (?) = 21

Now, in the first column; 18 + 17 + 22 = 57

In the second column; 23 + 19 + (?) = 57 ⇒ (?) = 15

Similarly, in the third column; 16 + 21 + (?) = 57 ⇒ (?) = 20

So, from the above 15, 21, and 20 are the required numbers of the given figure. Hence, the second option is correct.

For non verbal reasoning must read the below topics:

About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.