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## Ten most important missing numbers questions and answers in reasoning

Ten most important   missing numbers questions and answers in box problems in Reasoning Analogy in various figures of different order and types discussed in this post. These types of problems are very very important for the exams like SSC CGL ,SSC CHSL , RRB NTPC and many other similar competitive exams.

# Ten most important missing numbers questions and answers in reasoning

## PROBLEM # 1 Since in 1st row we can write 3, 2 and 4  numbers to get 10 like this
( 3 × 2 ) + 4 = 6 + 4  = 10 (The number in last column  of 1st row )
And in 2nd row  ( 4 × 3 ) + 5 = 12 + 5 = 17, (The number in last column  of 2nd row )
In 3rd row ( 5 × 4 ) + 6 = 20 + 6 = 26 ,(The number in last column  of 3rd row )
Similarly ( 6 × 5 ) + 7 = 30 + 7 = 37 , (The number in last column  of 4th row )
So  " ? "   Will be replaced by 37 .
Therefore correct option will be (D)

Answer can be split into two parts, 1st part can be obtained by multiplying two given  numbers and second part can be obtained by adding these two numbers .
1st row
5 × 3  = 15 and 5 + 3 = 8 so 5 , 3 = 158
2nd row
9 × 1  = 9 and 9 + 1 = 10 so 9 , 1 = 910
3rd  row
8 × 6  = 48 and  8 +6 = 14  so 8 , 6 = 4814
4th row
4 × 4 = 16 and   4 + 4 = 8 so  4 , 4 = 168.
5th row
7 × 3 = 21 and 7 + 3 = 10 so 7 , 3 = 2110
So ?  Will be replaced by 2110.
Therefore correct option will be (A)

PROBLEM # 3

As the sum of 2nd and 3rd number in first and second rows in any particular column is equal to 1st element in that particular column so to get the value of " ? " . Take difference of first and second numbers column wise to get third number as follows.
44 +12 =  56,
48 + 30 = 78 ,
14 + ? = 65
➡️   ? = 65 - 14  = 51
Therefore correct option will be (C)

## PROBLEM # 4

Let us find relation between 3 and 18 , if we double the square of  3 ,we shall have 18.
2 × (3²) = 2 × 9 = 18 (The number in last column  of 1st row )
And in 2nd row if we double the square of  4 ,we shall have 32
2 × (4²) = 2 × 16 = 32, (The number in last column  of 2nd row)
In the same way increasing the number one by one then  third ,fourth and  fifth columns can be calculated like this

2 × (5²) = 2 × 25 = 50 (The number in last column  of 3rd row )
2 × (6²) = 2 × 36 = 72 (The number in last column  of 4th row )
2 × (7²)  = 2 × 49 = 98 (The number in last column  of 5th row )
Therefore correct option will be (C)

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## Formula a*b = (a × b) + (b - 1)

This the sum of two numbers , out of two ,1st number is product of two given  numbers and second  is the number one less than 2nd given number.

3 × 2 = (3 × 2) + (2 - 1) = 6 + 1 = 7
5 × 4 = (5 × 4) + (4 - 1) = 20 + 3 = 23
7 × 6 = (7 × 6) + (6 - 1) = 42 + 5 = 47
9 × 8 = (9 × 8) + (8 - 1) = 72 + 7 = 79
10 × 9 = (10 × 9) + (9 - 1) = 90 +8 = 98
Therefore correct option will be (C)

Suppose we have three numbers a , b and c then

## Formula for this puzzle is = (a × b) + b or  b(a + 1)

Put a = 2 and  b = 6 in above formula ,we get

1st Line = (2  × 6)   +  6  = 12   +   6   = 18
Put a = 4 and  b = 20 in above formula to get 2nd line,we get
(4  × 20) + 20 = 80   +  20  = 100
Put a = 5 and  b = 21 in above formula to get 3rd line,we get
(6 × 21) + 21 = 126 +  21  = 147
So required and correct answer will be  6.

## If in every row ,we add 1st and 3rd column and then multiply the sum with 2nd column, we shall have number in 4th column .

If we  consider three numbers a , b and c and start calculation by
Formula =  (a × b) + (b × c)  or b(a + c)  --------(1)

To get 1st line , put a = 1 , b = 2 and c = 3 in (1) , we get

1st Line =  (1×2) + (2×3) =2 + 6 = 8

To get 2nd line , put a = 2 , b = 3 and c = 4 in (1) , we get

2nd  Line =  (2×3) + (3×4) = 6 + 12 =  18

To get 3rd line , put a = 3 , b = 4 and c = 5 in (1) , we get

3rd Line =  (3×4) + (4×5) = 12 + 20  = 32

To get 4th line , put a = 4 , b = 5 and c = 6 in (1) , we get

4th Line =  (4×5) + (5×6) = 20 + 30  = 50

Similarly Last line can be calculated by putting a = 5 , b = 6 and c = 7 in (1) , we get

Last line  =  (5×6) + (6×7) = 30 + 42  = 72
Therefore correct option will be (D)

## PROBLEM # 8

### Case 1

If we choose   1st number  as 5 then look at the pattern  opposite to given smaller number

5  ×  3 =  15
8  ×  3 =  24
12 × 3  =  36
In this pattern we can conclude 12 ×3 = 36

### Case 2

If we choose   1st number  from ? then look at the opposite to given smaller number
?    ×  3 = 12
5   ×  3  = 15
8   ×  3  = 24
Therefore ? will be replaced  by 4.
Hence    4 ×  3  = 12

## This circle can be divided into two parts ,  1st part containing the number 4 ,5 ,6 and 7 and second part containing 7 , 9 ,11 and ?.            Now study  the opposite number of 4  which is 7 . Then study the relation between other numbers and its opposite number ,we find difference between 4 and 7 is 3 , difference between 5 and 9 is 4 , difference between 6 and 11 is 5  . so in this pattern we can find difference between ' ? '  and  7 must be 6 .
7 - ? =  2 means ? = 5
7 - 4 =  3
9 - 5 =  4
11 - 6 = 5 , the difference is increased by 1 every time .
?   - 7 = 6  means ? = 13
Either 5 or 13 should be the required number, but 5 is not given in any option.
So ? Will be replaced by 13 which is the required answer
Therefore correct option will be (4)

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