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Number Theory Level 3

p p and q q are the digits of a positive two digit integer such that p > q p > q and p − q = n . p-q=n.

If the 2 digit number p q ‾ \overline{pq} is divided by the sum of its digit, the quotient is 7 and the remainder is n n . Find the value of n n .


The answer is 3.

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Harsh Shrivastava by Harsh Shrivastava , 20, India

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1 solution

Harsha Vardhan
Mar 17, 2014

p - q=n
10p + q=7*(p+q) + n -> 3p - 6q=n
p - q = 3p - 6q
2p = 5q and since both p,q are positive integers between 0 & 9 only 2,5 will satisfy this. so p=5 and q =2


5 Helpful 0 Interesting 0 Brilliant 0 Confused

52, N=3

Abdelhameed Nasser - 7 years, 2 months ago

where you get 10p?

Rifqi Mukhammad - 6 years, 2 months ago

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arre bhai! 23 can be written as 2X10 + 3 likewise.......(place value yarr!)

Sarthak Rath - 6 years, 1 month ago

i'm sorry harsha i have get it now,thanks

Rifqi Mukhammad - 6 years, 2 months ago

I think the questioned asked for the value of n,if you had shown that p-q=n or 5-2=n or n=3,might've been better

Rifath Rahman - 5 years, 11 months ago

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