# Ten most important problems of Reasoning for competitive exams

**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 take 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

**c**

**orrect 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,

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 , 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

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**

**P**

**roblem # 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 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

(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

**Correct option is ( b )****82**### Do you like Missing number in box, Reasoning problem

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