Art of Problem Solving

2007 AMC 8 Problems/Problem 18: Difference between revisions

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==Video Solution==
==Video Solution==
https://youtu.be/7an5wU9Q5hk?t=2085
https://youtu.be/7an5wU9Q5hk?t=2085


==Solution==
==Solution==
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Note that the ones and thousands digits are, added together, <math>8</math>. (and so on...) So the answer is <math>\boxed{\textbf{(D)}\ 8}</math>
Note that the ones and thousands digits are, added together, <math>8</math>. (and so on...) So the answer is <math>\boxed{\textbf{(D)}\ 8}</math>
This is a direct multlipication way.
This is a direct multlipication way.
==Video Solution by WhyMath==
https://youtu.be/_goaFuScO6M
~savannahsolver


==See Also==
==See Also==
{{AMC8 box|year=2007|num-b=17|num-a=19}}
{{AMC8 box|year=2007|num-b=17|num-a=19}}
{{MAA Notice}}
{{MAA Notice}}

Revision as of 21:49, 20 April 2021

Problem

The product of the two $99$-digit numbers

$303,030,303,...,030,303$ and $505,050,505,...,050,505$

has thousands digit $A$ and units digit $B$. What is the sum of $A$ and $B$?

$\mathrm{(A)}\ 3 \qquad \mathrm{(B)}\ 5 \qquad \mathrm{(C)}\ 6 \qquad \mathrm{(D)}\ 8 \qquad \mathrm{(E)}\ 10$

Video Solution

https://youtu.be/7an5wU9Q5hk?t=2085


Solution

We can first make a small example to find out $A$ and $B$. So,

$303\times505=153015$

The ones digit plus thousands digit is $5+3=8$.

Note that the ones and thousands digits are, added together, $8$. (and so on...) So the answer is $\boxed{\textbf{(D)}\ 8}$ This is a direct multlipication way.

Video Solution by WhyMath

https://youtu.be/_goaFuScO6M

~savannahsolver

See Also

2007 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing