Question

Consider a number N = 2 1 P 5 3 Q 4 then the numbered of odered pairs ( P, Q) so that the number is divisible by 44 is

Answer 1

it is divisible by 44 means divisible by 4 and divisible by 11.

so, Q4 is divisible by 4. so, Q is an even number.

moreover,

N is divisible by 11.

so, P + 9 - Q-6 = 0

so, Q -P = 3

as Q is even number, Q = 0,2,4,6,8

as 0,2 are less than 3, then cant be the case.

so, Q = 4,6,8 and P = 1,3,5

so, ordered pairs are (1,4);(3,6);(5,8).

so, there are three ordered pairs..

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