Difference between revisions of "2011 AMC 10A Problems/Problem 4"
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<math> \textbf{(A)}\ 92\qquad\textbf{(B)}\ 98\qquad\textbf{(C)}\ 100\qquad\textbf{(D)}\ 102\qquad\textbf{(E)}\ 112 </math> | <math> \textbf{(A)}\ 92\qquad\textbf{(B)}\ 98\qquad\textbf{(C)}\ 100\qquad\textbf{(D)}\ 102\qquad\textbf{(E)}\ 112 </math> | ||
| − | == | + | ==Solution== |
We see that both sequences have equal numbers of terms, so reformat the sequence to look like: | We see that both sequences have equal numbers of terms, so reformat the sequence to look like: | ||
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\end{align*}</cmath> | \end{align*}</cmath> | ||
From here it is obvious that <math>Y - X = 102 - 10 = 92</math> | From here it is obvious that <math>Y - X = 102 - 10 = 92</math> | ||
| + | == See Also == | ||
| + | {{AMC10 box|year=2011|ab=A|num-b=3|num-a=5}} | ||
Revision as of 09:55, 8 May 2011
Let X and Y be the following sums of arithmetic sequences:
\begin{eqnarray*}X &=& 10+12+14+\cdots+100,\\ Y &=& 12+14+16+\cdots+102.\end[eqnarray*} (Error compiling LaTeX. Unknown error_msg)
What is the value of Y - X?
Solution
We see that both sequences have equal numbers of terms, so reformat the sequence to look like:
From here it is obvious that 
See Also
| 2011 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 | ||
