A five digit number n= a b c d e is such that when divided respectively by 2,3,4,5,6 the remainders are a, b, c, d, e . What is the remainder when n is divided by 100 ?

Step-by-step solution

aligned & a 0,1 , b 0,1,2 , c 0,1,2,3 , d 0, & 1,2,3,4 , e 0,1,2,3,4,5 aligned n is a five digit number, so a=1 and n must be odd. When n is divided by 5 the remainder is e or e-5 . So either d=e or (d, e)=(0,5) (i) When d=e then (d, e)=(1,1) or (3,3) de c (divisible by 4) b (divisible by 3) 11 3 0,1,2 33 1 Not possible So n=10311 or 11311 or 12311 Out of which n=11311 is correct when we check the condition of divided by 6 . (ii) When (d, e)=(0,5) then c=1, b is not possible. So n=11311