Ten most important problems of Reasoning for competitive exam Part1



Problem # 1


6  :  29   ::   24  :  ?
(a)  109         (b)   129       (c)    119        (d) 99


Solution 

6 is related to 29 in the same way 24 will be related to ? , It means we have to apply same mathematical operations to 24 to get ?.
So if we multiply 6 with 5  and then subtract 1 from result obtained in previous step like this ( 6 × 5 )  - 1 which will be equal to 29.
Same operation we have to apply  to 24.
( 24 × 5 ) - 1 = 120 - 1 =  119

So Correct  option is ( c ) 119



                         Problem # 2

5  :  100   ::   7  :  ?

(a)      135     (b) 91         (c)   196         (d) 49


Solution


Because in 1st case if we take Square of  5 then multiply it with 4 we shall have 100.
5² × 4 = 25 × 4 = 100
Same procedure will be applied in 3rd number by taking square of 7 then multiply it with 4
7² × 4 = 49 × 4 = 196

Correct  option is  ( c  ) 196

Problem # 3

6  :  18   ::   4  :  ?

(a)    4       (b)  6        (c)   8         (d) 10


Solution 

Divide  6² by 2
6² ÷ 2 = 36 ÷ 2 = 18
Similarly divide 4² with 2
I.e.  4² ÷ 2 = 16 ÷2 = 8
Divide the square of 1st number by 2 to get 2nd number. Similarly square of third number and then divide it by 2 to to get the number equal to? Since square of 4 is 16 then divided by 2 to get it.
6² ÷ 2 = 36 ÷ 2 = 18

4² ÷ 2 = 16 ÷ 2 = 8 

Correct  option is (  c ) 8


Problem # 4

18  :  30   ::   36  :  ?

(a)    64       (b)  62        (c)  54          (d) 66


Solution  

 (18 × 2 ) - 6  = 36 - 6 = 30
 (36 × 2 ) - 6  = 72 - 6 = 66
Multiply 1st number (18) with 2 and then subtract 6 from it
18 × 2 =  36 - 6 = 30
Similarly Multiply 3rd number ( 36 ) with 2 and then subtract 6 from it ,

36 × 2 = 72 - 6 = 66

correct  option is ( d) 66


Problem # 5

12  :  20   ::   30  :  ?

(a)  48         (b)   42       (c)   15         (d) 35


Solution 
Method 1  

Split 12  =  3 × 4 
split  20  = 4 × 5, 
Split  30 =  5 × 6,  
Here study these factors (3 , 4 ) , (4 ,5 ) ,(5 ,6 ) so next pair will be  ( 6 , 7 ) 
, It means ? Will be replaced by the number 6 × 7 = 42

Method 2 


12 will be written as square of 3 plus 3 , 20 will be written as square of 4 plus 4 ,30 will be written as square of 5 plus 5, so next number will be written as square of 6 plus 6 which is equal to 42 , Therefore   required option will be 42
                         Or
Make continuous factors 3 and ,4 and 5 ,5 and 6 and 6 and 7 of 12,20,30 and 42 respectively 
12 = 3×4  , 
20 = 4 × 5  ,
30 = 5 × 6 so 
42 = 6×7

Add same number to its square to get next number 
Or multiply next number to the number
 9  = 3² + 3   ,
 20 = 4² +4 ,
 30 = 5² + 5
42 = 6² + 6
Correct  option is ( b ) 42

 Problem # 6


12  :  54   ::   15  :  ?

(a)    64       (b)   69       (c) 56           (d) 67


Solution

(1st number ) × 5 - 6 = 2nd number
(12×5) - 6 = 54
Multiply 3rd number with 5 then subtract 6 from it
(3rd number ) × 5 - 6 = 4th  number
(15×5) - 6 = 69
Multiply first number ( 12 ) with 5 then subtract 6 from it to get 2nd number ( 54 ) ,   Similarly   Multiply third  number ( 15 ) with 5 then subtract 6 from it.
( 1 2 × 5  ) - 6 = 60 - 6 = 54
( 1 5 × 5  ) - 6 = 75 - 6 = 69

Correct  option is ( b) 69

Problem # 7

6  :  5   ::   8  :  ?

(a) 6          (b)10          (c) 2           (d)4 


Solution
Add 4 to 1st number and divide it with 2 to get 2nd number( 6 + 4 )/2 = 5
Similarly in 2nd case Add 4 to 3rd number then divide the resultant with 2 to get 4th number
( 8 + 4 )/2 = 6
Correct  option is ( a ) 6


Problem # 8

29  :  319  ::    23 :  ?


    (a) 115          (b)  252        (c)  151          (d) 46

Solution

Add both the digits of first number  i.e. 2 and 9 then multiply it with first number to get second number. similarly in the third number add both the digits I.e  2 and 3  and multiply it with 3rd number to get fourth number.
29 × ( 2+9 ) = 29 × 11 = 319
23 × ( 2+3 ) = 23 ×  5  = 115

So 253 is the right option (a) 115

Problem # 9

6  :  64   ::   11  :  ?


(a) 127          (b) 124         (c) 144           (d) 169


Solution

Add 2 to 1st given number and take its Square to get 2nd number. Similarly add 2 to 3rd number and take it square to get fourth number.
(6 +2 )² = 8² = 64
(11+2)² = 13² = 169



Correct  option is ( d ) 169

Problem # 10

36  :  50   ::   64  :  ?

(a)70           (b) 82         (c)78            (d) 72


Solution

Take Square Root of 1st number and add 1 to it then add 1 to  its Square to get 2nd number.
Similarly take square root of 64 add 1 to its square  root and take it square and add 1  to get 4th number.
36 = 6² --->  (6 + 1)² +1 = 50 ,

 64 = 8² ------>. ( 8+1)²+1 = 82
√36 = 6 add 1 to it = 7 , square this number = 49 +1 = 50
√64 = 8 add 1 to it = 9 , square this number = 81 +1 = 82

So  the right option is (b) 82

 Correct option is ( b ) 82






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Missing number in box, Reasoning problem

Reasoning of missing number in box problems

PROBLEM #  1

Reasoning of missing number in box problem

Step 1. Subtract the number in first column from the number in third column of every row. i. e. C3 - C1 = Step 2 . Multiply the the above difference with 3 to get the numbers in second column of every row i. e. C2 = 3S1st row 48 - 28 = 20 × 3 = 602nd row 7 - 5 = 2 × 3 = 63rd row 27 - 14 = 13 × 3 = 394th row 16 - 7 = 9 × 3 = 27 Hence required number is 27


PROBLEM #  2

Reasoning of missing number in box problem

Take the square of addition of  the elements of 1st three rows of 1st column like this
Square(1 + 4 + 2 ) = sqr (7) = 49

Take the Take the square of addition of  the elements of 1st three rows of 1st column like this
Square(4 + 2 + 2 ) = sqr (8) = 64

Take the square of addition of  the elements of 1st three rows of 1st column like this
Square(? + 5 + 3 ) = sqr (? + 8 ) = 169
sqr (? + 8 ) = sqr (13)
? + 8 = 13
? = 5
So required number will be 5

PROBLEM #  3

Reasoning of missing number in box problem
Multiply all the numbers in the first three rows of every column and then divide the product by 2 to get the number in last row like this
(5×2×8)÷2 = 80÷2 = 40
(5×4×3)÷2 = 60÷2 = 30
(2×1×10)÷2 = 20÷2 = 10
So required number will be 10

PROBLEM #  4



Adding both the numbers in second and third rows then multiply it with the number in First row to get the number in in last row the process will be  repeated for all the three columns
( 6 + 7 ) × 5 = 65
( 3 + 2 ) × 4 = 20
( ? + 4 ) × 9 = 45
This implies ( ? + 4 ) = 45/9 = 5
? = 5-4 = 1
Hence required number is 1

PROBLEM #  5


Decrease the numbers in first two columns of every row by 1 then multiply it to get the number in third column of every row. 
1st Row  ( 8 - 1) ×  3  = 7 × 3 = 21
2nd Row  ( 6 - 1) ×  5 = 5 × 5 = 25
3rd Row  ( 12 - 1) ×  2 =11 × 2 = 22
Hence required answer is 22

PROBLEM #  6


Add 1st two rows of each column to multiply with the number in 3rd column to get fourth number in every row. 
(5 + 4 ) × 2 =  18
(6 + 3 ) × 3 =  27
(12 + 4 ) × ? = 96
         16 × ? = 96
? = 6
Hence required number is 6

PROBLEM #  7



First of all multiply  1st three numbers  in every Column then add the sum of 1st three  numbers in every row to  get the numbers in 4th row. i. e. formula for this problem is [ abc+(a+b+c) ]
[ ( 3+4+5+(3×4×5 ) ] = 12 + 60 = 72
[ ( 2+5+6+(2×5×6 ) ] = 13 + 60 = 73
[ ( 5+9+1+(5×9×1 ) ] = 15 + 45 = 60
Hence  required number is 60

Also study these missing number series questions

PROBLEM #  8


Decrease both the numbers in first and second columns of every row then multiply the reduced number to get the numbers in third column of every row
{ 8 - 1 }×{ 6 - 1 } = 35
{ 6 - 1 }×{ 4 - 1 } = 15 
{ 7 - 1 }×{ 5 - 1 } = 24
Hence required number is 24.

PROBLEM #  9



Decrease the numbers in first column of every row and increase the numbers in second column of every row when multiplying both the reduced number of first and second column to get the numbers in third column of every row

{ 6 - 1 }×{ 8 + 1 } =  45
{ 4 - 1 }×{ 6 + 1 } =  21
{ 7 - 1 }×{ 5 + 1 } = 36
Hence required number is 36

PROBLEM #  10



Total of 1st row is  3 + 6 + 8 = 17
Total of 2nd row is  5 + 6 + 8 = 17
Total of 3rd row is  4 + 7 + ? = 17
Therefore replacing ? with 6 to get required answer.

So these were the most important box problems for many competitive exams



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Ten most important questions of Reasoning Analogy in missing numbers in various figures

 we are going to discuss Ten most important  questions of  missing number  in Reasoning Analogy in various figures

PROBLEM # 1
                  Find missing Number ?

10 most tricky puzzle with their solutions
Since in 1st row we can write 2,3 and 4 these numbers to get 10 like this
 ( 3 × 2 ) + 4 = 6 + 4  = 10
And in 2nd row  ( 4 × 3 ) + 5 = 12 + 5 = 17, 
In 3rd row ( 5 × 4 ) + 6 = 20 + 6 = 26
Similarly ( 6 × 5 ) + 7 = 30 + 7 = 37
So  " ? "   Will be replaced by 37 .
 पहली संख्या को दूसरी संख्या से गुणा करने   के बाद उसमें तीसरी संख्या जोड़ देने से हमें    बराबर है  चिन्ह के दायीं  तरफ की संख्या मिलती है

                   PROBLEM # 2

               Find missing Number ?


                         10 most tricky puzzle with their solutions
Let us find relation between 3 and 32 , if we double the square of  3 ,we shall have 18. 
2 × ( 3^2) = 2 × 9 = 18
And in 2nd row if we double the square of  4 ,we shall have 32
2 × ( 4^2) = 2 × 16 = 32
In the same way third ,fourth and  fifth column can be calculated like this 

          2 × ( 5^2) = 2 × 25 = 50
          2 × ( 6^2) = 2 × 36 = 72
          2 × (7^2)  = 2 × 49 = 98
So 98 is required answer.
 सबसे पहले जो संख्या दी गई है उसका वर्ग करें और उसको 2 से गुणा कर दीजिए हमें दाएं तरफ की संख्या मिल जाएगी ।


                PROBLEM # 3



           Find missing Number ?



As the sum of first and second number in first and second rows in any particular column is equal to third element in that particular column so to get the value of " ? " . Add first and second numbers column wise to get third number as follows.
56 - 12 =  44,
78 - 30 = 48 ,
65 - ? = 14 ➡️  ? = ? = 65 - 14  = 49 
So 49 is required number .
इस   प्रश्न को हल करने के लिए हम column wise  सोचेंगे । हम हर column में पहली संख्या से दूसरी संख्या को घटाकर तीसरी संख्या प्राप्त कर सकते हैं जैसे कि 
56 - 12 = 44 ,
78 - 30 = 48 , इसी तरह से
 65 - 51  = 14

                    PROBLEM # 4
              Find missing Number ?

10 most tricky puzzle with their solutions

Answer can be splited into two parts, 1st part can be obtained multiplying given two  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 5 + 3 = 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.
 हमारे पास दो संख्याएं दी गई है पहले उन दोनों संख्याओं को गुणा करेंगे तो दाएं तरफ की संख्या के पहले दो अंक (  अगर गुणा करने से 2 अंक बनते हो तो) लिखे जाएंगे फिर उन दोनों संख्याओं को जमा करेंगे तो दाएं और दी गई संख्या के आखिरी दो अंक लिखे जाएंगे ।
 .
PROBLEM # 5
Find missing Number ?


Formula a*b = (a × b) + (b - 1)

This the sum of two numbers , out of 1st number is product of two given two numbers and second number 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
पहले दोनों दी गई संख्याओं को गुणा करें फिर दूसरी संख्या से एक घटाने के बाद गुणा करने के बाद जो उत्तर आया था  ।उसमें जमा कर दें ,आपको दाएं तरफ की संख्या मिल जाऐगी ।

                      PROBLEM # 6
                  
Find the missing number ?
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
तीसरे स्थान पर दी गई संख्या को दूसरे स्थान पर दी गई संख्या से भाग करें तथा जो उत्तर आएगा उसमें से एक घटाएं, हमें पहले स्थान पर दी गई संख्या मिल जाएगी

                       PROBLEM # 7
Find missing Number ?


10 most tricky puzzle with their solutions

If in every row ,we add 1st and 3rd column and then multiply the sum with 2ndcolumn, we shall have number in 5th 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
Hence Required  and correct answer will be 72
पहले दूसरे column  ब  दूसरे तीसरे column को आपस में गुणा करें , गुणा करने के बाद जो उत्तर आऐंगे  उनको जमा कर दें हमें चौथे column की संख्या मिल जाएगी ।

                 PROBLEM # 8
            
Find the missing number ?

Case 1


If we choose   1st Line  from 5 then look at the pattern  line wise 
                              5  ×  3 = 15
               8  ×  3 = 24
               12 × 3  =  36

In this pattern we can conclude 12 ×3 = 36

Case 2

If we choose   1st Line  from ? then look at the pattern  line wise

                               ?    ×  3 = 12
                 5   ×  3  = 15
                    8   ×  3  = 24   
Therefore ? will be replaced  by 4.
Hence    4 ×  3  = 12

  PROBLEM # 9
Find missing Number ?

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 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 everytime .
 ?   - 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 
Hence  option ( b)  is the correct option

PROBLEM # 10
                     Find missing Number ?

We shall try every possible relation between different numbers given either row wise or column wise . It is found that there is no relation if we consider First row . 
 After elemination of 1st row we can develop a relation between 2nd ,3rd and 4th row which is multiplying the 2nd and 3rd numbers then double it to get 4th number column wise .
 2 × (7 × 4 ) = 2 × 28 = 56
2 × ( 15 × 6 ) = 2 × 90 = 180
2  × ( 8 ×  ?  ) = 80 
So ? = 5
So correct options will be  (d ) 5.

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Ten most important problems of missing numbers in Reasoning Analogy part 2



Let us discuss series of missing numbers and missing terms and their  solutions in reasoning analogy .

Problem # 1

This series consists of two alternate series 1st series consist of number 1,3, 5 and 7 and second series consist of  the series 2 ,5 ,8,?

So in 1st series there is difference of 2, so next number in the series must be 2 greater than 7 that is 9 .
In the 2nd series  we observed a difference of 3 show the next number must be 11 that is 3 greater than 8 the last term therefore the last two terms of the series 11 and 9

The correct option is  ( a ) 11,9

Problem # 2

Find the next number? 

This series is also the combination of two series one with the number  2, 48 ,16 ,32 and second series consist of these numbers 6, 9 13 ,18 ,?  . So ? Will be filled out using 2nd series not from 1st series.

Observing 2nd series carefully ,In  second series numbers are increased by  3 ,4 and 5 ,so next Increment should be of 6. This implies next number should be  24 with an increment of 6.

The correct option is  ( a ) 

Problem # 3


Observe carefully all the numbers in the series are prime number , so  next prime number after 37 will be 41 .This implies that  ?  will be replaced by 41.

The correct option is  ( c ) 

Problem # 4

which is wrong number  ?

All the numbers in this series are consist of three digits numbers and Middle digit is the sum of first and last digit in all the numbers except one that is 342 in this case 3 + 2 is equal to 5 not equal to 4 .So  correct option is option is  (c) ,this is the wrong number in the series .

The correct option is  ( C ) 

Problem # 5

Every number in this series is the sum of its two  preceding number plus 3.

14  = ( 7 + 4 ) + 3
24 = ( 14 + 7 ) + 3
41 = ( 24  +14 ) + 3
?   = ( 41 + 24 ) + 3 = 65+3 = 68

The correct option is  (  C ) 

Problem # 6

Which is wrong number  ?

This series consists of triplet ,that is every third number is product  its two preceding numbers

  As third  number 10 is the product of 2 and 5, sixth number  18 is the product of fourth (3) and fifth (6 ) numbers .

So ninth number of the series  must be the product of seventh and  eighth numbers. 4 × 7 = 28 instead of 30

The correct option is  ( C ) 

Problem # 7


Find the next number? 

Here second  number is the sum of the digits of first number the forth number is the sum of digits of third number similarly every even positioned number is  the sum of its preceding number's digits question  mark will be replaced by the sum of 5 + 3 that is 8

The correct option is  ( a ) 

Problem # 8

Find the next number? 

Writing 3 = 2² - 1

Writing 8 = 3² - 1

Writing  15 = 4² - 1

Writing 24 = 5² - 1


Show next number should be  6² - 1 ( square minus 1 ) that is 35

Writing  6² - 1 = 35

The correct option is  (2 ) 

Problem # 9

Which is wrong  number? 

Every number in this series is the double of its preceding number

 So double of 1 is   2 , double of 2 is 4 ,double of 4 should be 8 ( instead of 7 ) , double of 8 is 16 and double of 16 should be 32 .  So 7 is the wrong number in this series.

The correct option is  ( 1 ) 

Problem # 10

Find the next number? 

In the series every number is the the cube of its  position plus 1 .

Since

  2 =  1³ + 1

   9 =  2³ + 1

  28 =  3³ + 1

  65  =  4³ + 1

  126 =  5³ + 1

  In the same way next number of the series must be  6³ + 1 = 216 + 1 = 217

The correct option is  ( 1 ) 

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