Difference between revisions of "2016 AMC 10A Problems/Problem 6"

Revision as of 02:18, 27 June 2023

Problem

Star lists the whole numbers $1$ through $30$ once. Emilio copies Ximena's numbers, replacing each occurrence of the digit $2$ by the digit $1$ . Star adds her numbers and Emilio adds his numbers. How much larger is Ximena's sum than Emilio's?

$\textbf{(A)}\ 13\qquad\textbf{(B)}\ 26\qquad\textbf{(C)}\ 102\qquad\textbf{(D)}\ 103\qquad\textbf{(E)}\ 110$

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 $10\cdot 10+1\cdot 3=\boxed{\textbf{(D) }103.}$

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

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.

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 == Problem ==
-Ximena lists the whole numbers <math>1</math> through <math>30</math> once. Emilio copies Ximena's numbers, replacing each occurrence of the digit <math>2</math> by the digit <math>1</math>. Ximena adds her numbers and Emilio adds his numbers. How much larger is Ximena's sum than Emilio's?
+Star lists the whole numbers <math>1</math> through <math>30</math> once. Emilio copies Ximena'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 Ximena'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>

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