## Easy sum

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Raiyan Jamil
Posts: 138
Joined: Fri Mar 29, 2013 3:49 pm

### Easy sum

The product of two numbers is 1000 . If non of the numbers have a zero as their digits , what is their sum ?
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asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### Re: Easy sum

The sum is $2^{3}+5^{3}=8+125=133$

Labib
Posts: 411
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### Re: Easy sum

@Asif Please do elaborate how you eliminated other possible answers when posting solutions like these.
Here is a explanation to why the only possible answer is $125$.
Notice that - $1000 = 2^3*5^3$.
Assume that one of the two factors is $a = 2^n*5^m$ where $0\leq n,m\leq 3$.
If $n \geq 1$ and $m \geq 1$, then the last digit of $a$ will be $0$ which would be contradictory to the statement.
Therefore $n$ and $m$ cannot simultaneously be greater than $1$. So whether it is a factor of $5$ or a factor of $2$.
The same is true for its compliment as well.
I'd leave the rest for you to deduce.
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes