A 3-digit number 4p3 is added to another 3-digit number 984 to give the four-digit number 13q7, which is divisible by 11. then, (p + q) is :
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For a number to be divisible by 11, difference of the sum of its alternate digits must be divisible by 11,
The only number of the form 13q7 that are divisible by 11 is 1397 where (1+9)-(3+7) = 0 is divisible by 11
Hence, q = 9
Also as we can see from the sum above,
p + 8 = q (There is no carry as 9+4=13 in hundreds place)
=> p +8=9
p = 1
Hence p+q = 1+9 = 10
The only number of the form 13q7 that are divisible by 11 is 1397 where (1+9)-(3+7) = 0 is divisible by 11
Hence, q = 9
Also as we can see from the sum above,
p + 8 = q (There is no carry as 9+4=13 in hundreds place)
=> p +8=9
p = 1
Hence p+q = 1+9 = 10
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