2024 AMC 10A Problems

2024 AMC 10A (Answer Key) Printable versions: Wiki • AoPS Resources • PDF
Instructions This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. You will receive 6 points for each correct answer, 2.5 points for each problem left unanswered if the year is before 2006, 1.5 points for each problem left unanswered if the year is after 2006, and 0 points for each incorrect answer. No aids are permitted other than scratch paper, graph paper, ruler, compass, protractor and erasers (and calculators that are accepted for use on the SAT if before 2006. No problems on the test will require the use of a calculator). Figures are not necessarily drawn to scale. You will have 75 minutes working time to complete the test.
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Problem 1

What is the value of $9901\cdot101-99\cdot10101?$

$\textbf{(A)}~2\qquad\textbf{(B)}~20\qquad\textbf{(C)}~200\qquad\textbf{(D)}~202\qquad\textbf{(E)}~2020$

Solution

Problem 2

A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form $T=aL+bG,$ where $a$ and $b$ are constants, $T$ is the time in minutes, $L$ is the length of the trail in miles, and $G$ is the altitude gain in feet. The model estimates that it will take $69$ minutes to hike to the top if a trail is $1.5$ miles long and ascends $800$ feet, as well as if a trail is $1.2$ miles long and ascends $1100$ feet. How many minutes does the model estimates it will take to hike to the top if the trail is $4.2$ miles long and ascends $4000$ feet?

$\textbf{(A) }240\qquad\textbf{(B) }246\qquad\textbf{(C) }252\qquad\textbf{(D) }258\qquad\textbf{(E) }264$

Solution

Problem 3

What is the sum of the digits of the smallest prime that can be written as a sum of $5$ distinct primes?

$\textbf{(A) }5\qquad\textbf{(B) }7\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad\textbf{(E) }13$

Solution

Problem 4

The number 2024 is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum?

$\textbf{(A) }20\qquad\textbf{(B) }21\qquad\textbf{(C) }22\qquad\textbf{(D) }23\qquad\textbf{(E) }24$

Solution

Problem 5

XXX

$\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }$

Solution

Problem 6

XXX

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Solution

Problem 7

The product of three integers is 60. What is the least possible positive sum of the three integers?

$\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }13$

Solution

Problem 8

XXX

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Solution

Problem 9

XXX

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Solution

Problem 10

XXX

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Solution

Problem 11

XXX

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Solution

Problem 12

XXX

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Solution

Problem 13

XXX

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Solution

Problem 14

XXX

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Solution

Problem 15

XXX

$\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }$

Solution

Problem 16

XXX

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Solution

Problem 17

XXX

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Solution

Problem 18

XXX

$\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }$

Solution

Problem 19

XXX

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Solution

Problem 20

XXX

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Solution

Problem 21

XXX

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Solution

Problem 22

XXX

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Solution

Problem 23

XXX

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Solution

Problem 24

XXX

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Solution

Problem 25

XXX

Solution

2024 AMC 10A (Problems • Answer Key • Resources)
Preceded by 2023 AMC 10B Problems	Followed by 2024 AMC 10B Problems
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All AMC 10 Problems and Solutions

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2024 AMC 10A Problems

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

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

See also