Question

let n be the largest integer that is the product of exactly 3 distinct prime numbers x, y and 10 x + y where x and y are the digits what is the sum of digits of n

Answer 1

Given, x and y are digits such that x, y and 10x + y are prime

numbers and their product is n largest possible.

so x = 7 and y = 3 WHY????

since n is largest possible product so choosing x

as largest prime digit i.e 7

and y can’t be 7 as 10x+y would be divisible by 7 but given it is

a prime number and it can’t be 5 also as 10x+y=75 not a prime thus y=3

which makes 10x+y=73 i.e. a prime number as required

Now, n = (7)*(3)*(73) = 1533

hence sum of digits of n = 1+5+3+3=12.