The no of ordered pairs (P,Q ) for which 213P43Q6 is divisible by 99 are
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Divisibility by 9 : Sum of the digits must be divisible by 9.
Divisibility by 11 : Difference of even and odd digits must be either divisible by 11 or equal to 0.
213P43Q6 = P+Q+19
(P+Q) = 8 , 17 ..... (1)
Similarly , 213P43Q6 = 9+Q-(10+P) = Q-P-1
(Q-P) = 1 , 12 ...... (2)
(P,Q) = (8,9) (only integral solution)
Divisibility by 11 : Difference of even and odd digits must be either divisible by 11 or equal to 0.
213P43Q6 = P+Q+19
(P+Q) = 8 , 17 ..... (1)
Similarly , 213P43Q6 = 9+Q-(10+P) = Q-P-1
(Q-P) = 1 , 12 ...... (2)
(P,Q) = (8,9) (only integral solution)
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