Question : Which of the following pairs of non-zero values of p and q make the 6-digit number 674pq0 divisible by both 3 and 11?
Option 1: p = 2 and q = 2
Option 2: p = 5 and q = 4
Option 3: p = 4 and q = 2
Option 4: p = 5 and q = 2
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Correct Answer: p = 5 and q = 2
Solution :
Given number = 674pq0
As 674pq0 divisible by 3
So, 6 + 7 + 4 + p + q + 0 is also divisible by 3.
⇒ 17 + p + q also divisible by 3
⇒ Possible values of p + q = 4, 7, 10, 13, 16
p = 2 and q = 2, and p = 5 and q = 2 is satisfying the given equation.
For p = 2 and q = 2,
The number is 674220
So, 6 + 4 + 2 - 7 - 2 = 3 Not divisible by 11.
For p = 5 and q = 2
The number is 674520
And, 6 + 4 + 2 - 7 - 5 = 0 divisible by 11
Hence, the correct answer is p = 5 and q = 2.
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