Question

If ABC × DEED = ABCABC; where A, B, C, D and E are different digits, what are the values of D and E? 

(a) D = 2, E = 0 (b) D = 0, E = 1 (c) D = 1, E = 0 (d) D = 1, E = 2

Answer 1

(c) ABC × DEED = ABCABC

We know that, when we write any Number in form of ABCABC then that number must be divisible

by 13 , 11 and 7 or ABCABC is multiple of 1001

So, 1001 = DEED

1001 = 13 × 11 × 7

 ABC × DEED = ABC ABC

⇒ ABC × 1001 = ABC ABC

On comparing

D = 1, E = 0