Difference between revisions of "2021 AMC 12B Problems/Problem 10"
Soysoy4444 (talk | contribs) (Created page with " The sum of the first <math>37</math> integers is given by <math>n(n+1)/2</math>, so <math>37(37+1)/2=703</math>. Therefore, <math>703-x-y=xy</math> Rearranging, <math>xy+x+...") |
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Therefore, the difference <math>y-x=31-21=10</math>, choice E). | Therefore, the difference <math>y-x=31-21=10</math>, choice E). | ||
+ | ~ SoySoy4444 |
Revision as of 20:44, 11 February 2021
The sum of the first integers is given by
, so
.
Therefore,
Rearranging,
Looking at the possible divisors of ,
and
are within the constraints of
so we try those:
Therefore, the difference , choice E).
~ SoySoy4444