Difference between revisions of "2015 AMC 12A Problems/Problem 10"
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Use [[SFFT]] to get <math>(x+1)(y+1)=81</math>. The terms <math>(x+1)</math> and <math>(y+1)</math> must be factors of <math>81</math>, which include <math>1, 3, 9, 27, 81</math>. Because <math>x > y</math>, <math>x+1</math> is equal to <math>27</math> or <math>81</math>. But if <math>x+1=81</math>, then <math>y=0</math> and so <math>x=\boxed{\textbf{(E)}\ 26}</math>. | Use [[SFFT]] to get <math>(x+1)(y+1)=81</math>. The terms <math>(x+1)</math> and <math>(y+1)</math> must be factors of <math>81</math>, which include <math>1, 3, 9, 27, 81</math>. Because <math>x > y</math>, <math>x+1</math> is equal to <math>27</math> or <math>81</math>. But if <math>x+1=81</math>, then <math>y=0</math> and so <math>x=\boxed{\textbf{(E)}\ 26}</math>. | ||
+ | |||
+ | == Video Solution == | ||
+ | https://youtu.be/ba6w1OhXqOQ?t=4512 | ||
+ | |||
+ | ~ pi_is_3.14 | ||
== See Also == | == See Also == | ||
{{AMC12 box|year=2015|ab=A|num-b=9|num-a=11}} | {{AMC12 box|year=2015|ab=A|num-b=9|num-a=11}} |
Revision as of 19:11, 15 January 2021
Contents
Problem
Integers and
with
satisfy
. What is
?
Solution
Use SFFT to get . The terms
and
must be factors of
, which include
. Because
,
is equal to
or
. But if
, then
and so
.
Video Solution
https://youtu.be/ba6w1OhXqOQ?t=4512
~ pi_is_3.14
See Also
2015 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 12 Problems and Solutions |