Difference between revisions of "2024 AIME II Problems"

Revision as of 21:13, 8 February 2024

2024 AIME II (Answer Key) Printable version \| AoPS Contest Collections • PDF
Instructions This is a 15-question, 3-hour examination. All answers are integers ranging from $000$ to $999$ , inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, calculators and computers are not permitted.
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Problem 1

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Problem 2

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Problem 3

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Problem 4

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Problem 5

Solution

Problem 6

Solution

Problem 7

Let $N$ be the greatest four-digit integer with the property that whenever one of its digits is changed to $1$ , the resulting number is divisible by $7$ . Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$ . Find $Q+R$ .

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Find the number of triples of nonnegative integers $(a, b, c)$ satisfying $a + b + c = 300$ and

$a^2 b + a^2 c + b^2 a + b^2 c + c^2 a + c^2 b = 6,000,000.$

Solution

Problem 12

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Problem 13

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Problem 14

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Problem 15

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@@ Line 33: / Line 33: @@
 ==Problem 7==
+Let <math>N</math> be the greatest four-digit integer with the property that whenever one of its digits is changed to <math>1</math>, the resulting number is divisible by <math>7</math>. Let <math>Q</math> and <math>R</math> be the quotient and remainder, respectively, when <math>N</math> is divided by <math>1000</math>. Find <math>Q+R</math>.
 [[2024 AIME II Problems/Problem 7|Solution]]
@@ Line 56: / Line 56: @@
 ==Problem 11==
+Find the number of triples of nonnegative integers <math>(a, b, c)</math> satisfying <math>a + b + c = 300</math> and
+<cmath>a^2 b + a^2 c + b^2 a + b^2 c + c^2 a + c^2 b = 6,000,000.</cmath>
 [[2024 AIME II Problems/Problem 11|Solution]]

2024 AIME II (Problems • Answer Key • Resources)
Preceded by 2024 AIME I	Followed by 2025 AIME I
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Difference between revisions of "2024 AIME II Problems"

Revision as of 21:13, 8 February 2024

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

See also