Two Natural Numbers, p and q, do not end in zero....

[bazookaworm]

Ok, I have no idea what section this would belong in and I am only in grade 7, I cannot find the answer to this question, could anyone help? I do not get this question at all :?

The Question
Two Natural Numbers, p and q, do not end in zero. The product of any pair, p and q, is a power of 10. If p>q the last digit of p - q cannot be...

A) 1
B) 3
C) 5
D) 7
E) 9

Thanks In Advance.( I am not looking for a direct answer, but how I could arrive to it.) A direct answer would be nice though

 

[stapel]

Try stuff. For instance:

Pick various powers of 10. Factor them in ways that do not involve ten-times-something, or a hundred-times-something, etc. For instance, 10² = (4)(25), where neither of 4 or 25 ends in zero.

See what patterns you can find.

Eliz.

 

[bazookaworm]

Thanks for the reply, would the answer be 5?( or maybe its 1 :? )

Thanks In Advance

 

[Denis]

Seems somewhat "tough" as a grade 7 question...anyhoo:
the multiplication p * q = a power of 10, so:
pq = 10^k where k is any integer greater than 0

5^k * 2^k = 10^k
So p = 5^k and q = 2^k
Therefore, p ends with 5, and q ends with 2 or 4 or 6 or 8

Is that enough?

 

[bazookaworm]

Ok..Is the answer A(1) then?

Thanks In Advance

 

[Denis]

C'mon Bazook:
"Therefore, p ends with 5, and q ends with 2 or 4 or 6 or 8"

When p > q, we have:
5 - 2 = 3
5 - 4 = 1
5 - 6 = 9 : like 25 - 16
5 - 8 = 7 : like 25 - 18

 

[bazookaworm]

So it is one? I knew it!!! No...actually I don't, I don't even understand what you're doing. Sorry

 

[Denis]

C'mon Bazook...once more:
from p which ends with the digit 5,
you subtract q which ends with the digit 2 or 4 or 6 or 8:
will you at any time get an answer that ends with digit 5 ?