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The rightmost non-zero digit in

 

\( \begin{align*} &(1001001)(1010101)+(989899)(1001001)\\ &\qquad -(1001)(989899)-(1010101)(1001) \end{align*}\)

 

is  a, and it is followed by b zeroes. Find the ordered pair (a,b)

 Apr 22, 2018
edited by gueesstt  Apr 22, 2018
 #1
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Hey! I'm back,

 

So, if you look at \((1001001)(1010101)+(989899)(1001001)\),

 

You can see that both share a commom 1001001

 

This means we can factor out the 1001001:


\(1001001(1010101+989899) \)

 

You can easily tell the number in the paranthesis is 2000000.

 

The same goes with\( -(1001)(989899)-(1010101)(1001)\)

 

We can factor out the -1001:

 

\(-1001(989899+1010101)\)

 

Once againg, we have very easy numbers we can do in our head:

 

\(-1001(2000000)\)

 

Combining those two expressions, we have:

 

\( 1001001(2000000)-1001(2000000)\)

 

Once again, we can factor out the 2000000

 

\(2000000(1001001-1001)\)

 

Finalizing, we have:

 

\(2000000\cdot{1000000}\)

 

The number we are looking for is 2000000000000, or 2 trillion.

 

So a, is 2, and b is 12

 

The ordered pair is (2,12)

 Apr 22, 2018
 #2
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Thank you!

gueesstt  Apr 22, 2018

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