Reasoning: Machine Input-Output Questions — Set 41

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.

1. What is the addition of three numbers obtained in step 1?
   47
   37
   50
   67
   57
   Option 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:
   = 2³ + 2³ + 1³ = 17
   Reverse the digits: 71
   Taking the entire second digits together:
   = 2³ + 3³ + 2³ = 43
   Reverse the digits = 34
   In third step:
   = 7 × 1² = 07, …. 3 × 4² = 48
   In fourth step:
   Reversing the digits: 84 – 70 = 14

   

   For 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:
   = 1³ + 2³ + 2³ = 17
   Reverse the digits: 71
   Taking the entire second digits together:
   = 2³ + 1³ + 4³ = 73
   Reverse the digits: 37
   For step 3:
   = 7 × 1² = 07, … 3 × 7² = 147
   For step 4:
   Reversing the digits: 741 – 70 = 671
   Hence, addition of three numbers obtained in step 1:
   = 12 + 21 + 24
   = 57

    

2. Find the difference of two numbers obtained in step 3?
   120
   100
   140
   150
   90
   Option C
   Hence, difference of two numbers in step 3:
   = 147 – 7
   = 140
   

    

3. Find the multiplication of the two numbers obtained in step 2?
   2627
   2526
   2675
   2647
   2567
   Option A
   Hence, multiplication of numbers in step 2:
   = 71 × 37
   = 2627
   

    

4. Find the multiplication of unit and tens digit of a number which is obtained in step 4?
   8
   7
   6
   5
   4
   Option B
   Hence, multiplication of unit and tens digit of a number in step 4:
   = 7 × 1
   = 7
   

    

5. Which of the following number is obtained in step 4?
   571
   471
   771
   671
   371
   Option D
   Hence, the number obtained in step 4 is 671.
   

    

(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.



6. Which number is greater in step 1?
   53
   25
   63
   60
   Other than options given
   Option 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 = 1

   In second step:
   From the first digits:
   5 × 5 – 1 = 24
   From the second digits:
   8 × 2 – 1 = 15

   In 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 = 1

   In second step:
   From the first digits:
   6 × 2 – 2 = 10
   From the second digits:
   3 × 5 – 1 = 14

   In third step:
   a) 1 + 0 = 1
   b) 1 + 4 = 5
   In fourth step:
   1 + 5 = 6

   Hence, 63 is the greatest number in step 1.

    

7. What is the second smallest number obtained in any step of given input?
   8.5
   7.5
   5
   10.5
   7
   Option C
   5 is the second smallest number in any step of given input.

    

8. Find the difference between sum of numbers obtained in step 1 and sum of numbers obtained in all other steps?
   61
   67
   89
   73
   76
   Option 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
   

    

9. What is the difference between the second largest number and the smallest number obtained in any steps?
   24
   18
   15
   29
   21
   Option A
   Second largest number = 25
   Smallest number = 1
   Difference = 25 – 1 = 24
   

    

10. What is the average of numbers obtained in last two steps?
    4
    5
    9
    7
    None of these
    Option A
    Average of numbers obtained in last two steps = (1+5+6)/3 = 12/3 = 4