Knewton challenge!

[GmatKiss]

If A,BCD is a four-digit positive integer such that A,BCD is equal to the product of the two-digit number AB and the three digit number ABC, which of the following two-digit numbers cannot be a factor of A,BCD? (Note: the first digit of a number cannot be equal to 0.)

i. AD
ii. CD
iii. CA

(A) None
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

[moonraker]

For this take an example based solution.

if ABCD = AB x ABC it makes more sense to take AB = 10 as the value of D would be decided as 0 then.
now for ABC take 101 or 102.
It will give u the number 1010 or 1020 as ABCD.

Now AB = 10 and CD = 10 or 20 and both AB and CD divide the original number ABCD.

The only issue with my solution is that I am unable to prove the validity of the option None as these examples check for AD and CD divisibility.

Also if anyone takes the number 1030 or 1040 the answer to this solution will not come.

the correct ans to this question must be C..

Please do update whether this is right.