Difference between revisions of "2011 AMC 10A Problems/Problem 4"
Coolmath34 (talk | contribs) (→Solution 1) |
Coolmath34 (talk | contribs) (→Note) |
||
| Line 16: | Line 16: | ||
From here it is obvious that Y - X = 102 - 10 = <math>\boxed{92 \ \mathbf{(A)}}</math>. | From here it is obvious that Y - X = 102 - 10 = <math>\boxed{92 \ \mathbf{(A)}}</math>. | ||
| − | =Note= | + | ===Note=== |
Another way to see this is to let the sum <math>12+14+16+...+100=x.</math> So, the sequences become | Another way to see this is to let the sum <math>12+14+16+...+100=x.</math> So, the sequences become | ||
<cmath>\begin{align*} | <cmath>\begin{align*} | ||
Revision as of 22:25, 30 January 2018
Let X and Y be the following sums of arithmetic sequences:
What is the value of Y - X?
Contents
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 Y - X = 102 - 10 = 
.
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. 
