Let p, q be two-digit numbers neither of which are divisible by 10 . Let r be the four-digit number by putting the digits of p followed by the digits of q (in order). As p, q vary, a computer prints r on the screen if gcd (p, q)=1 and p+q d

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Let p, q be two-digit numbers neither of which are divisible by 10 . Let r be the four-digit number by putting the digits of p followed by the digits of q (in order). As p, q vary, a computer prints r on the screen if gcd (p, q)=1 and p+q divides r . Suppose that the largest number that is printed by the computer is N . Determine the number formed by the last two digits of N (in the same order).

Quantrex Academy · Accepted Answer

Correct answer: 13

aligned & r=100 r+q & r+q r=100 r+q & r+q 99 r aligned But gcd (r+q, r)=1 array ll & r+q 99 & r+q=33 or 99 array For N to be maximum r+q=99 Where r=89, q=13 Answer 13.

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