IIT JEE , AIEEE Forum - Mathematics , Algebra

sandeepramesh

let the no. be 10x+y implies 10x+y = 4(x+y) + 3 implies 2x = y+1

implies the number is odd.

Also 10x+y = 3xy+5 as the parity of LHS is odd and 5 is odd implies x is even.

as 10x and 5 are divisible by 5 implies y and 3xy leave the same remainder when divided by 5.

implies 3x shd leave a remainder 1 when divided by 5

implies x= 2 or 7

but x is even implies x = 2

putting in the eqn

20 + y = 6y + 5 implies y = 3.

Hence the number is 23 which is an odd prime :) thus answer is b :)

PS i tried to avoid to say the word mod :D