Difference between revisions of "2019 AMC 10A Problems/Problem 2"
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==Solution 3== | ==Solution 3== | ||
Because we know that <math>5^3</math> is a factor of <math>15!</math> and <math>20!</math>, the last three digits of both numbers is a 0, this means that the difference of the hundreds digits is also <math>\boxed{\text{(A) }0}</math>. | Because we know that <math>5^3</math> is a factor of <math>15!</math> and <math>20!</math>, the last three digits of both numbers is a 0, this means that the difference of the hundreds digits is also <math>\boxed{\text{(A) }0}</math>. | ||
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| + | ==Solution 4== | ||
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| + | We can clearly see that <math>20! \equiv 15! \equiv 0 \pmod{100}</math>, so <math>20! - 15! \equiv 0 \pmod{100}</math> meaning that the last two digits are equal to <math>00</math> and the hundreds digit is <math>0</math>, or <math>\boxed{\text{(A)}}</math>. | ||
==See Also== | ==See Also== | ||
Revision as of 18:16, 23 June 2021
Problem
What is the hundreds digit of 
Video Solution 1
Education, The Study of Everything
Video Solution 2
~savannahsolver
== Video Solution == 3 https://youtu.be/zfChnbMGLVQ?t=3899
~ pi_is_3.14
Solution 3
Because we know that 
is a factor of 
and 
, the last three digits of both numbers is a 0, this means that the difference of the hundreds digits is also 
.
Solution 4
We can clearly see that 
, so 
meaning that the last two digits are equal to 
and the hundreds digit is 
, or 
.
See Also
| 2019 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 | ||
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