Difference between revisions of "2019 AMC 10A Problems/Problem 2"
Scrabbler94 (talk | contribs) (Solution 2 is wrong since divisibility by 100 doesn't imply the hundreds digit of their difference is 0.) |
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<math>\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }4\qquad\textbf{(E) }5</math> | <math>\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }4\qquad\textbf{(E) }5</math> | ||
− | == Solution == | + | ==Video Solution 1== |
− | + | https://youtu.be/J4Bqztwjyxw | |
− | ==Video Solution== | + | Education, The Study of Everything |
+ | |||
+ | |||
+ | |||
+ | ==Video Solution 2== | ||
https://youtu.be/V1fY0oLSHvo | https://youtu.be/V1fY0oLSHvo | ||
~savannahsolver | ~savannahsolver | ||
+ | |||
+ | == Video Solution == 3 | ||
+ | https://youtu.be/zfChnbMGLVQ?t=3899 | ||
+ | |||
+ | ~ pi_is_3.14 | ||
+ | |||
+ | ==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>. | ||
+ | |||
+ | |||
+ | ==Solution 4== | ||
+ | |||
+ | 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>. | ||
+ | |||
+ | --abhinavg0627 | ||
+ | |||
+ | |||
+ | ==Solution 5== | ||
+ | |||
+ | <math>20!= 2432902008176640000</math> | ||
+ | <math>15!= 1307674368000</math> | ||
+ | |||
+ | Subtract | ||
+ | |||
+ | -dragoon | ||
==See Also== | ==See Also== |
Latest revision as of 14:12, 13 August 2022
Contents
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 .
--abhinavg0627
Solution 5
Subtract
-dragoon
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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