## 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

**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,

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

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

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 the right option is (b) 82

**Correct option is ( b )**

**82**

**ReasoningProblems #11**

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**Twelve-Figures-Problems#3**

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