Question

If m and n are positive integers such that mn = 4000 and if neither m or n contains the digit 0, then m-n could be
(a) 93
(b) 135
(c) 234
(d) 492
(e) 996

Answer 1

As tedious as it sounds, it would help to list all the factors of 4000, excluding the ones containing a 0.

Answer 2

But that's just my opinion. There might be a quicker, more convenient way about this.

Answer 3

In any case, the only factors of 4000 that don't have a 0 as a digit are 32 and 125.

Answer 4

if m= 125 and n= 32, m-n = 125-32 = 93

Answer 5

thanks guys

Answer 6

but i'm still wondering if there is a shorter way

Answer 7

since neither m nor n contain any zeros, 2 and 5 cannot be factors together for either. Thus separate out the factors 2 and 5.
1000 = 10*10*10 = 8*125
so factors of 4*1000 = 4*8* 125 = 32*125.
m and n should be 125 and 32 respectively.
You can skip out the redundant steps to shorten the solution.
without trees this is the shortest way I suppose.

Answer 8

to compute faster you could try option matching
if no no. has 0 then factors need to be of form last digit 5(odd) and any even number..now their dfference is odd..only 1st 2 options available..if difference has 5 as last digit then other no. must have 0 as last digit which should not be the case..so only 93 is possible! :D