Which of the following pairs of non-zero values of p and q make 6-digit number 674pq0 divisible by both 3 and 11?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e.p = 5 and q = 2.
Concept used:
Divisibility rule of 3: a number is completely divisible by 3 if the sum of its digits is divisible by 3
Divisibility rule of 11: the given number can only be completely divided by 11 if the difference of the sum of digits at odd position and sum of digits at even position in a number is 0 or 11
Calculations:
By option method:
Taking option (4), we have p = 5 and q = 2
Hence sum of digits = 6 + 7 + 4 + 5 + 2 + 0 = 24
24 is divisible by 3
Now, for 11 we have: 6 + 4 + 2 - (7 + 5 + 0) = 0
Required difference = 0
Therefore, the value of p = 5 and q = 2