please solve this Q

Question

Question:-

Consider the following program fragment

a = 0
for (x = 1; x < 31; ++x)
for (y = 1; y < 31; ++y)
  for (z = 1; z < 31; ++z)
    if (((x + y + z)%3) = =0)
    a = a + 1;
printf("%d”, a);

the output of the above given program is

Option (A) : 3000

Option (B) : 1000

Option(C) : 27000

Option(D) : None of these

Comments

Is it 9000..

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There are 4 ways multiple of 3 can be formed by 3 numbers. When each number is divisible by 3; when each number leaves 2 as remainder when divided by 3; when each number leaves 1 as remainder when divided by 3 ; when a number leaves 1, the next leaves 2 and the next leaves 0 as remainder when divisible by 3. Calculating the number of ways for each case is easy and that gives the answer.

Answer 1

The ans is D : none of this

It is given to us that :

a = 0
for (x = 1; x < 31; ++x)
for (y = 1; y < 31; ++y)
  for (z = 1; z < 31; ++z)
    if (((x + y + z)%3) = =0)   <-This statement will execute 30*30*30 times.
    a = a + 1;
It will execute 27000 times.

out of this for one complete iteration of the inner most loop if we see we will get 10 values for which the inner most condition will be satisfied and the value of a will be incremented. for 1st iteration:

1,1,1 ;1,1,4;1,1,7;1,1,10;1,1,13;1,1,16;1,1,19;1,1,22;1,1,25;1,1,28; i.e(31-1)/3=10

10 iterations because only 10 times we get a num which is one more than the multiple of 3 in the first iteration as see the value of x and y is fixed i.e 1+1 =2 so to satisfy the condition we need 1,4,7,so on so it is possible only for 10 values in the given range(arithmetic progression with common diff 3).

Next time also value of x and y will be fixed =1+2=3. Then the reqd no would be 3,6,9... so on for all iterations.

Total no of times the value of a will be incremented is 30*30*10=9000

So ans is 9000 and option D

Comments

The two upper loop will run 30*30 times the last loop will run 10 times so total 9000 will be answer

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for (z = 1; z < 31; ++z)

here z is preincrement so inside the loop minimum value of z should be 2 not 1

same for x,y  

??

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@Gurdeep Sainithe increment happens after the loop has executed we test the condition and then go inside the loop and then update is done.. so the thing that it is preincrement would not have any effect as such on the value of x,yor z inside the loop