Difference between revisions of "2016 AMC 10A Problems/Problem 6"
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== Problem == | == Problem == | ||
| − | + | Star lists the whole numbers <math>1</math> through <math>30</math> once. Emilio copies Star's numbers, replacing each occurrence of the digit <math>2</math> by the digit <math>1</math>. Star adds her numbers and Emilio adds his numbers. How much larger is Star's sum than Emilio's? | |
<math>\textbf{(A)}\ 13\qquad\textbf{(B)}\ 26\qquad\textbf{(C)}\ 102\qquad\textbf{(D)}\ 103\qquad\textbf{(E)}\ 110</math> | <math>\textbf{(A)}\ 13\qquad\textbf{(B)}\ 26\qquad\textbf{(C)}\ 102\qquad\textbf{(D)}\ 103\qquad\textbf{(E)}\ 110</math> | ||
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For every tens digit 2, we subtract 10, and for every units digit 2, we subtract 1. Because 2 appears 10 times as a tens digit and 2 appears 3 times as a units digit, the answer is <math>10\cdot 10+1\cdot 3=\boxed{\textbf{(D) }103.}</math> | For every tens digit 2, we subtract 10, and for every units digit 2, we subtract 1. Because 2 appears 10 times as a tens digit and 2 appears 3 times as a units digit, the answer is <math>10\cdot 10+1\cdot 3=\boxed{\textbf{(D) }103.}</math> | ||
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| + | ==Video Solution (HOW TO THINK CRITICALLY!!!)== | ||
| + | https://youtu.be/qrgPsA9AQLA. (short and simple!) | ||
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| + | Education, the Study of Education. | ||
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==Video Solution== | ==Video Solution== | ||
https://youtu.be/XXX4_oBHuGk | https://youtu.be/XXX4_oBHuGk | ||
| − | + | https://youtu.be/8i_NYG3aRxE | |
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==See Also== | ==See Also== | ||
{{AMC10 box|year=2016|ab=A|num-b=5|num-a=7}} | {{AMC10 box|year=2016|ab=A|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 02:18, 27 June 2023
Contents
Problem
Star lists the whole numbers 
through 
once. Emilio copies Star's numbers, replacing each occurrence of the digit 
by the digit . Star adds her numbers and Emilio adds his numbers. How much larger is Star's sum than Emilio's?
Solution
For every tens digit 2, we subtract 10, and for every units digit 2, we subtract 1. Because 2 appears 10 times as a tens digit and 2 appears 3 times as a units digit, the answer is 
Video Solution (HOW TO THINK CRITICALLY!!!)
https://youtu.be/qrgPsA9AQLA. (short and simple!)
Education, the Study of Education.
Video Solution
https://youtu.be/XXX4_oBHuGk https://youtu.be/8i_NYG3aRxE
See Also
| 2016 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
