2016 AMC 12A Problems
2016 AMC 12A (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
Problem 1
What is the value of ?
Problem 2
For what value of does
?
Problem 3
The remainder function can be defined for all real numbers and
with
by
,
where denotes the greatest integer less than or equal to
. What is the value of
?
Problem 4
The mean, median, and mode of the 7 data values are all equal to
. What is the value of
?
Problem 5
Goldbach's conjecture states that every even integer greater than 2 can be written as the sum of two prime numbers (for example, ). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?
Problem 6
A triangular array of 2016 coins in the first row, 2 coins in the second row, 3 coins in the third row, and so on up to coins in the
th row. What is the sum of the digits of
?
Problem 7
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Problem 8
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Problem 9
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Problem 10
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Problem 11
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Problem 12
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Problem 13
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Problem 14
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Problem 15
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Problem 16
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Problem 17
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Problem 18
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Problem 19
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Problem 20
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Problem 21
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Problem 22
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Problem 23
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Problem 24
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Problem 25
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