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# help?

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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