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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