**Directions (1-5): Study the given information carefully and answer the given questions:**

An input-output is given in different steps. Some mathematical operations are done in each step. No mathematical operation is repeated in next step.

- What is the addition of three numbers obtained in step 1?
4737506757Option E

Solution:

In first step:

a) 8 × 5 – 6 × 3, ….. 9 × 3 – 4 × 1, ….. 2 × 7 – 1 × 2

……. 40 – 18 = 22, ….. 27 – 4 = 23, ….. 14 – 2 = 12

In second step:

Taking the entire first digits together:

= 2^{3}+ 2^{3}+ 1^{3}= 17

Reverse the digits: 71

Taking the entire second digits together:

= 2^{3}+ 3^{3}+ 2^{3}= 43

Reverse the digits = 34

In third step:

= 7 × 1^{2}= 07, …. 3 × 4^{2}= 48

In fourth step:

Reversing the digits: 84 – 70 = 14For step 1:

a) 6 × 5 – 3 × 6, …… 6 × 4 – 3 × 1, …… 6 × 5 – 2 × 3

…… 30 – 18 = 12, ….. 24 – 3 = 21, ….. 30 – 6 = 24

For step 2:

Taking the entire first digits together:

= 1^{3}+ 2^{3}+ 2^{3}= 17

Reverse the digits: 71

Taking the entire second digits together:

= 2^{3}+ 1^{3}+ 4^{3}= 73

Reverse the digits: 37

For step 3:

= 7 × 1^{2}= 07, … 3 × 7^{2}= 147

For step 4:

Reversing the digits: 741 – 70 = 671

Hence, addition of three numbers obtained in step 1:

= 12 + 21 + 24

= 57 - Find the difference of two numbers obtained in step 3?
12010014015090Option C

Hence, difference of two numbers in step 3:

= 147 – 7

= 140

- Find the multiplication of the two numbers obtained in step 2?
26272526267526472567Option A

Hence, multiplication of numbers in step 2:

= 71 × 37

= 2627

- Find the multiplication of unit and tens digit of a number which is obtained in step 4?
87654Option B

Hence, multiplication of unit and tens digit of a number in step 4:

= 7 × 1

= 7

- Which of the following number is obtained in step 4?
571471771671371Option D

Hence, the number obtained in step 4 is 671.

- Which number is greater in step 1?
53256360Other than options givenOption C

Solution:

In first step:

a) 8 – 3 = 5, 10 – 2 = 8

b) 9 – 4 = 5, 4 – 2 = 2

c) 6 – 5 = 1, 9 – 8 = 1In second step:

From the first digits:

5 × 5 – 1 = 24

From the second digits:

8 × 2 – 1 = 15In third step:

a) 2 + 4 = 6

b) 5 + 1 = 6

In fourth step:

6 + 6 = 12

Further, 1 + 2 = 3

In first step:

a) 8 – 2 = 6, 5 – 2 = 3

b) 4 – 2 = 2, 6 – 1 = 5

c) 5 – 3 = 2, 8 – 7 = 1In second step:

From the first digits:

6 × 2 – 2 = 10

From the second digits:

3 × 5 – 1 = 14In third step:

a) 1 + 0 = 1

b) 1 + 4 = 5

In fourth step:

1 + 5 = 6Hence, 63 is the greatest number in step 1.

- What is the second smallest number obtained in any step of given input?
8.57.5510.57Option C

5 is the second smallest number in any step of given input. - Find the difference between sum of numbers obtained in step 1 and sum of numbers obtained in all other steps?
6167897376Option D

Sum of numbers obtained in step 1: 63 + 25 + 21 = 109

Sum of numbers obtained in other steps: 10 + 14 + 1 + 5 + 6 = 36

Difference between them = 73

- What is the difference between the second largest number and the smallest number obtained in any steps?
2418152921Option A

Second largest number = 25

Smallest number = 1

Difference = 25 – 1 = 24

- What is the average of numbers obtained in last two steps?
4597None of theseOption A

Average of numbers obtained in last two steps = (1+5+6)/3 = 12/3 = 4

**(Directions 6 – 10): A string of numbers is given as input. The further steps given are obtained by applying certain logic. Numbers of step II have been obtained by using at least 1 digit of each number in step I. Each step is a resultant of previous step only.**