Difference between revisions of "2024 AMC 8 Problems/Problem 8"
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~ cxsmi (minor formatting edits) | ~ cxsmi (minor formatting edits) | ||
+ | ==Solution 2 (Slightly less BRUTE FORCE)== | ||
+ | Continue as in Solution 1 to get <math>7</math>, <math>8</math>, or <math>10</math> dollars by the 2nd day. The only way to get the same dollar amount occurring twice by branching (multiply by <math>2</math> or adding <math>3</math>) from here is if <math>7+3=10\cdot 2</math> or <math>7+3=8\cdot 2</math> which both aren't true. Hence our answer is <math>3\cdot2=\boxed{\textbf{(D)\ 6}}</math>. | ||
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+ | ~ Sahan Wijetunga | ||
==Video Solution 1 (easy to digest) by Power Solve== | ==Video Solution 1 (easy to digest) by Power Solve== |
Revision as of 20:50, 26 January 2024
Contents
[hide]Problem
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
Solution 1 (BRUTE FORCE)
How many values could be on the first day? Only dollars. The second day, you can either add dollars, or double, so you can have dollars, or . For each of these values, you have values for each. For dollars, you have dollars or , and for dollars, you have dollars or $. Now, you have values for each of these. For dollars, you have dollars or , for dollars, you have dollars or , for dollars, you have dollars or , and for dollars, you have dollars or .
$ and $ repeat leaving you with different values.
~ cxsmi (minor formatting edits)
Solution 2 (Slightly less BRUTE FORCE)
Continue as in Solution 1 to get , , or dollars by the 2nd day. The only way to get the same dollar amount occurring twice by branching (multiply by or adding ) from here is if or which both aren't true. Hence our answer is .
~ Sahan Wijetunga
Video Solution 1 (easy to digest) by Power Solve
https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=L83DxusGkSY
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=alDY4yhaEEg
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.