Difference between revisions of "2011 AMC 10A Problems/Problem 4"
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X = 10 \ + \ &12 + 14 + \cdots + 100\\ | X = 10 \ + \ &12 + 14 + \cdots + 100\\ | ||
\end{align*}</cmath> | \end{align*}</cmath> | ||
− | From here it is obvious that Y - X = 102 - 10 = | + | From here it is obvious that <math>Y - X = 102 - 10 = \boxed{92 \ \mathbf{(A)}}</math>. |
===Note=== | ===Note=== |
Revision as of 17:03, 14 January 2020
Contents
Problem
Let X and Y be the following sums of arithmetic sequences:
What is the value of Y - X?
Solution 1
We see that both sequences have equal numbers of terms, so reformat the sequence to look like:
From here it is obvious that .
Note
Another way to see this is to let the sum So, the sequences become
Like before, the difference between the two sequences is
Solution 2
We see that every number in Y's sequence is two more than every corresponding number in X's sequence. Since there are 46 numbers in each sequence, the difference must be:
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.