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## Missing number in box Reasoning problem, How to solve various circle problems

Reasoning of missing number in box problems, circle problems  and triangle problems will be discussed with the help of 10 most important examples. Some of these examples are of  4 × 4  order and other are of  4 × 3 orders.

# Reasoning of missing number in box problems in Uniteted State

## PROBLEM #  1

### Formula

Every row has been written as the cube of certain number. Because 4096 is the cube of 18, 6859 is the cube of 19 , 8000 is the cube of 20  similarly 926? will also be  the cube of any number. Look carefully 1st row is the cube of 18, then 2nd row is the cube of 19, 3rd row is the cube of 20 . So in this way 4th row must be  the cube of 21.

### Calculation

18³ = 4096
19³ = 6859
20³ = 8000
21³ = 9261
Hence value of question mark will be 1.
Option (D)1 is correct option.

## PROBLEM #  2

### Formula

Multiply the number in 2nd row with 100 and add it to the product of numbers in 1st and 2nd rows.

### Calculation

6*100 + (4*8) = 632
3*100 + (9*2) = 318
7*100 + (5*9) = 745
Option (A)745 is correct option.

## PROBLEM #  3

This reasoning problem consists of three figures and every figure have three numbers associated to it . Two numbers are on the upper line of each box and one number is at the bottom of the dark box.  Look at last figure , it have ? in its centre . So the solution of this problem is to find the value of question mark using two numbers associated to it .

But the main problem is how to utilised  these two numbers to get the value of question mark?
Now watch carefully the 1st two figures . Since these figures have some values of numbers in dark box .
Now we have to find or search the  formula for these three numbers in each figure to utilised them in any possible way to get number in  dark box .
The same formula will be applicable to third figure to find out the value of question mark.
Formula :- The DIFFERENCE of squares of both the numbers in empty box in upper line in every figure is equal to  number in dark box in lower line.
Solution:-

9²  - 6² = 81 - 36 = 45 (1st Figure)

8²  - 2² = 64 - 4 = 60 (2nd Figure)

7²  - 3² = 49 - 9 = 40  (3rd Figure)

Option (1)40  is correct option.

## PROBLEM #  4

This reasoning problem consists of three figures and every figure have three numbers associated to it . Two numbers are on the upper line of each box and one number is at the bottom of the dark box.  Look at last figure , it have ? in its centre . So the solution of this problem is to find the value of question mark using two numbers associated to it .

But the main aim is how to utilised  these two numbers to get the value of question mark?
Now watch carefully the 1st two figures . Since these figures have some values of numbers in dark box .
Now we have to find or search the  formula for these three numbers in each figure to utilised them in any possible way to get number in  dark box .
The same formula will be applicable to third figure to find out the value of question mark.
Formula :- The SUM of squares of both the numbers in empty box in upper line in every figure is equal to  number in dark box in lower line.
Solution:-

9²  + 6² = 81 + 36 = 117 (1st Figure)

8²  + 2² = 64 + 4 = 68 (2nd Figure)

7²  + 3² = 49 + 9 = 58 (3rd Figure)

Option (1)58 is correct option

## PROBLEM #  5

This figure consist of four squares around  one big square. Look carefully in this big square every number in it is perfect cube. And if we multiply the square roots of  two adjacent numbers then we shall have the number attached to big square between these two numbers whose square root had been multiplied.

√49  ×  √4 =  7  × 2 = 14 (The number at bottom line in the box)
√4  ×  √36 =  2  × 6 =  12 ( The number at leftmost box )
√36  ×  √? =   6  × √? = 30 ( The number at uppermost box )

√?  = 30/6 = 5, squaring both sides

? = 25 ( The number at uppermost box)
Similarly

√?  ×  √49 = 35
√?  = 35/7
√?  = 5,  squaring both sides
? = 25  (The number at rightmost box )

Option (A)25  is correct option

## PROBLEM # 6

This figure consist of four squares around  one big square. Look carefully in this big square every number in it is perfect cube. And if we multiply the square roots of  two adjacent numbers then we shall have the number attached to big square between these two numbers whose cube root had been multiplied.
∛343  ×  27 =  7 × 3 = 21( The number at rightmost box )
∛27  ×  ∛125 =  3  × 5 = 15 (The number at bottom line in the box)
∛125  ×  ? =  5  ×   ∛? = 10 ( The number at leftmost box )
×  ? = 10
?  = 10/5
? = 2 , cubing both sides
? = 8
Similarly

?  ×  343 =   ?  × 7  = 14

? = 14/7 = 2 cubing  both sides

? = 8 ( The number at uppermost box )

Option (C)8  is correct option

## PROBLEM #  7

This reasoning problem have two figures and every figure have five number attached to it . Four numbers are at the corner of each figure and one number is at the middle of the same figure.
Since second figure have question mark in its centre . So the solution of this problem is to find the value of question mark using four numbers associated to it .
But the main problem is how to utilised these four numbers to get the value of this question mark?
Now watch carefully the 1st two figures . since these figures have some values of middle numbers.
Now we have to find or search the  formula for these four numbers in each figure to utilised them in any possible way to get middle or central number.
The same formula will be applicable to third figure to find out the value of question mark.
Formula:-   Add all the numbers in the corner of each figure  to get value of the number in the middle.
Solution:-
√4 + √16 + √9 + √25 + 4 = 2 + 4 + 3 + 5 = 14 (Middle number in 1st figure).
√9 + √49 + √36 + √36 + √1 = 3 + 7 + 6 + 1 = 17 (Middle number in 1st figure).

Option (3)17  is correct option

## Reasoning of missing number in circle problems

PROBLEM #  8

This circle consists of four quadrants and every  quadrant consists of three numbers . And every quadrant have two numbers in outer part and one  number  in the inner part . To find the value of question mark  "?"  , we shall use two numbers which are in the outer part to calculate the value of the number which is in the inner part of every quadrant .

Step 1.   Take sum of the squares of both the numbers (8 and 4 ) in outer part of  this quadrant.

Step 2. Take the magnitude of difference of both the numbers in outer part of  this quadrant.

Step 3. Divide the result obtained in step 1 with the result obtained in step 2 to get the value of the number (20) in inner part of this quadrant.

### Calculation

(8² + 4² ) ÷ ( |8 - 4 |) = ( 64 + 16 ) ÷ 4 = 80 ÷ 2 = 20

Step 1.   Take sum of the squares of both the numbers ( 7 and 5 ) in outer part of  this quadrant.

Step 2. Take the magnitude of difference of both the numbers in outer part of  this quadrant.

Step 3. Divide the result obtained in step 1 with the result obtained in step 2 to get the value of the number (37) in inner part of this quadrant.

### Calculation

(5² + 7² ) ÷ (|5 - 7 |) = ( 25 + 49 ) ÷ 2 = 74 ÷ 2 = 37

Step 1.   Take sum of the squares of both the numbers ( 10 and 6 ) in outer part of  this quadrant.

Step 2. Take the magnitude of difference of both the numbers in outer part of  this quadrant.

Step 3. Divide the result obtained in step 1 with the result obtained in step 2 to get the value of the number (34) in inner part of this quadrant.

### Calculation

(10² + 6² ) ÷ ( |10 - 6| ) = ( 100 + 36 ) ÷ 4 = 136 ÷ 4 = 34

Step 1.   Take sum of the squares of both the numbers ( 10 and 6 ) in outer part of  this quadrant.

Step 2. Take the magnitude of difference of both the numbers in outer part of  this quadrant.

Step 3.  Divide the result obtained in step 1 with the result obtained in step 2 to get the value of the number (34) in inner part of this quadrant.

### Calculation

(6² + 4² ) ÷ ( |6 - 4 |) = ( 36 + 16 ) ÷ 2 = 52 ÷ 2 = 26

Option (3)26 is right option

## PROBLEM #  9

This  big circle is  divided into eight parts and  there is also one number written between  any  two numbers towards outer side of these two numbers .  If we  add these  two adjacent  numbers then reverse of order of the result so obtained then this number will be equal to the number in small circle opposite to both these numbers .
8  +  6  = 14 ⟺  41 ( Reversing the order of digits)
6 + 11 = 17 ⟺  71  ( Reversing the order of digits)
11 + 10 =  21 ⟺ 12 ( Reversing the order of digits)
10 + 31 = 41 ⟺ 14 ( Reversing the order of digits)
31 + 12 = 43 ⟺ 34 ( Reversing the order of digits)
12 + 17 = 29 ⟺ 92 ( Reversing the order of digits)
17 + 5  = 22 ⟺ 22 ( Reversing the order of digits)
8  + 5 = 13  ⟺  31 = ? ( Reversing the order of digits)
Hence the value of  "? " will be 31

Option (B)13 is right option

## PROBLEM #  10

This reasoning problem consists of three figures and every figure have three numbers associated to it . So the solution of this problem is to find the value of question mark using other two numbers associated to it .
But the problem is how to utilised these two numbers to get the value of this question mark?
Now we have to find or search the  formula for these two numbers in each figure to utilised them in any possible way to get third number.
The same formula will be applicable to third figure to find out the value of question mark.
Formula :- One tenth of the product of  two outer numbers in each triangle is equal to third number .
1st Triangle
( 5 × 4 ) ÷ 10 = 20 ÷ 10 = 2 (Middle number in 1st triangle )
2nd Triangle
( 6 × 5 )  ÷ 10 = 30 ÷ 10 = 3 (Middle number in 2nd triangle )
3rd Triangle
( 15 × 6 )  ÷ 10 = 90 ÷ 10 = 9 (Middle number in 3rd triangle )

Option (3)9  is correct option

Ten Most Important Reasoning questions with answers for competitive exams of  series , box and other type with solutions have been discussed in this post . These types of problems are very helpful for cracking competitive exams like ssc cgl, ssc chsl and various Bank exams and many other similar exams. please feel free to comment your opinions

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