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Sopra Steria Aptitude Questions - Type 1 - Question 2


Q2. The following algorithm doubles the numbers in 2,4,6,8. For this what should be the minimum value in box number 12.
(n) means box number n.
      1          2           3           4           5            6           7           8          9           10         11          12
2
4
11
7
9
0
5
2
4
1
2
1

Step1: Initialization: Put the no in box (7) into box number 12.
Step2: Add: no in box (2) + no in box (2). Put the result in box (2).
Step3. Check: number in box number (12) leaves a remainder 1 when divided by 5.
Step4: Change : Increase box number in step 2 by 2.
Step 5: Multiply: Multiply no. in box(12) by 2.
Step6: Subtract: Decrease no. in box(12) by the no whose box no. is in box (3)














Solution

These types of problems can be easily solved by following the algorithm steps .
The initial values in the boxes are :

             1        2        3         4             5          6          7            8            9         10      11        12
2
4
11
7
9
0
5
2
4
1
2
1

We can consider the collection of boxes as an array. So the contents of the array are :
         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]
2
4
11
7
9
0
5
2
4
1
2
1




Step 1: Now initially after Step 1, the values in the array are :
         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]  
2
4
11
7
9
0
5
2
4
1
2
5


From here the iteration starts until the number in box (12) leaves a remainder 1 when divided by 5. We can rewrite the condition as :
                                (A[12] % 5 == 0)

Iteration 1 :
Step 2 : Add the number in box (2) and number in box (2) and put the result in box (2).
             This is can be well understood as :
                         A[2]  =  A[2]  + A[2]
                                  =   4  + 4
                         A[2]  =   8

Step 3 : Check  if  (A[12] % 5 == 0) then    EXIT.
             Here the condition is not fulfilled hence the algorithm controls move to Step 4.
                                    A[12] % 5
= 5 % 5
= 0

Step 4 : Increase box number in step 2 by 2.
             In this step, we are changing step 2.Now the box number will be (2 + 2 ) = (4).
             So the step 2 becomes                 
A[4]   =  A[4] + A[4]

Step 5: Multiply number in box 12 by 2.
                        i.e. A[12] = A[12] * 2;
                                          = 5 * 2
                                          = 10
            The Array becomes :

         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
7
9
0
5
2
4
1
2
10


Step 6 : Decrease no. in box(12) by the no whose box no. is in box (3) i.e.
                        A[12]   = A[12] –  A [A[3]]                = A[12] – A[11]
                                    = 10 – 2                                               = 8



The final array after iteration 1 becomes :
             
         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
7
9
0
5
2
4
1
2
8


Iteration 2 :
Step 2 :   A[4]   =  A[4] + A[4]           = 7 + 7
    A[4] =  14

Step 3 :. A[12] % 5    =  8 % 5            = 3
                        if  (A[12] % 5 == 0) = FALSE
            Hence the control moves to next step.

Step 4 :  Increase box number in step 2 by 2.
             In this step, we are changing step 2.Now the box number will be (4 + 2 ) = (6).
             So the step 2 becomes :
                        A[6]   =  A[6] + A[6]
          
Step 5 :  Multiply number in box 12 by 2.
                        i.e. A[12] = A[12] * 2;
                                          = 8 * 2
                                          = 16
            The Array becomes :
             
         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
14
9
0
5
2
4
1
2
16

Step 6 : Decrease no. in box(12) by the no whose box no. is in box (3) i.e.
                        A[12]   = A[12] –  A [A[3]]                = A[12] – A[11]
                                    = 16 – 2                                               = 14

The final array after iteration 2 is :

         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
14
9
0
5
2
4
1
2
14

Iteration 3 :
Step 2 :   A[6]   =  A[6] + A[6]           = 0 + 0
    A[6] =  0

Step 3 :. A[12] % 5    =  14 % 5          = 4
                        if  (A[12] % 5 == 0) = FALSE
            Hence the control moves to next step.

Step 4 :  Increase box number in step 2 by 2.
             In this step, we are changing step 2.Now the box number will be (6 + 2 ) = (8).
             So the step 2 becomes :
                        A[8]   =  A[8] + A[8]
          
Step 5 :  Multiply number in box 12 by 2.
                        i.e. A[12] = A[12] * 2;
                                          = 14 * 2
                                          = 28
            The Array becomes :

         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
14
9
0
5
2
4
1
2
28

Step 6 : Decrease no. in box(12) by the no whose box no. is in box (3) i.e.
                        A[12]   = A[12] –  A [A[3]]                = A[12] – A[11]
                                    = 28 – 2                                               = 26

The final array after iteration 2 is :
             
         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
14
9
0
5
2
4
1
2
26

Iteration 4 :
Step 2 :   A[8]   =  A[8] + A[8]           = 2 + 2
    A[8] =  4

Step 3 :. A[12] % 5    =  26 % 5          = 1
                        if  (A[12] % 5 == 0) = TRUE
            Hence the program exits..

So the final array becomes :
             
         A[1]    A[2]    A[3]     A[4]     A[5]    A[6]    A[7]     A[8]    A[9]     A[10]    A[11]    A[12]

2
8
11
14
9
0
5
4
4
1
2
26


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Answer


Numbers in box (12) = 26

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