If the number 750pq is completely divisible by 3 then maximum value of p+q is:a.15b.6c.18d.3
Question
If the number 750pq is completely divisible by 3 then maximum value of p+q is:
a. 15
b. 6
c. 18
d. 3
Solution
The divisibility rule of 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3.
Given the number 750pq, the sum of the known digits is 7 + 5 + 0 = 12.
Since 12 is divisible by 3, the sum of p and q must also be divisible by 3 for the entire number to be divisible by 3.
The maximum value for any single digit (p or q) is 9. Therefore, the maximum sum of p and q (p+q) that is also divisible by 3 is 18 (9+9).
So, the maximum value of p+q is 18.
Therefore, the answer is c. 18.
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