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2015 · Q10

What is the number of possible pairs of (P,Q) if the number 357P25Q is divisible by both 3 and 5?

Elementary MathematicsNumber System
  1. A7
  2. B6
  3. C5
  4. DNone of the above

Explanation

Divisibility by 5 forces Q ∈ {0, 5}. The digit sum 22 + P + Q must be a multiple of 3. For Q = 0: P ∈ {2, 5, 8} (3 values); for Q = 5: P ∈ {0, 3, 6, 9} (4 values). Total 3 + 4 = 7 pairs (option A).