경시 · AMC 대비 · 4단계 중 4

AMC 10 2024A 문제 25개

문제마다 원리부터 푸는 풀이와 처음 풀 수 있는 학년(CCSS 기준)이 있습니다.

AMC 10 2024A #1 7학년부터 arithmetic, algebra
What is the value of 9901·101-99·10101?
AMC 10 2024A #2 8학년부터 algebra, rate-ratio
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, whe…
AMC 10 2024A #3 4학년부터 number-theory
What is the sum of the digits of the smallest prime that can be written as a sum of 5 distinct primes?
AMC 10 2024A #4 6학년부터 arithmetic, number-theory
The number 2024 is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-dig…
AMC 10 2024A #5 6학년부터 number-theory
What is the least value of n such that n! is a multiple of 2024?
AMC 10 2024A #6 4학년부터 counting
What is the minimum number of successive swaps of adjacent letters in the string ABCDEF that are needed to change the st…
AMC 10 2024A #7 7학년부터 number-theory, arithmetic
The product of three integers is 60. What is the least possible positive sum of the three integers?
AMC 10 2024A #8 6학년부터 rate-ratio, algebra
Amy, Bomani, Charlie, and Daria work in a chocolate factory. On Monday Amy, Bomani, and Charlie started working at 1:00…
AMC 10 2024A #9 7학년부터 counting
In how many ways can 6 juniors and 6 seniors form 3 disjoint teams of 4 people so that each team has 2 juniors and 2 sen…
AMC 10 2024A #10 6학년부터 number-theory, arithmetic
Consider the following operation. Given a positive integer n, if n is a multiple of 3, then you replace n by n/3. If n i…
AMC 10 2024A #11 8학년부터 algebra, number-theory
How many ordered pairs of integers (m, n) satisfy √(n² - 49) = m?
AMC 10 2024A #12 6학년부터 arithmetic
Zelda played the Adventures of Math game on August 1 and scored 1700 points. She continued to play daily over the next 5…
AMC 10 2024A #13 8학년부터 geometry-2d, counting
Two transformations are said to commute if applying the first followed by the second gives the same result as applying t…
AMC 10 2024A #14 8학년부터 geometry-2d
One side of an equilateral triangle of height 24 lies on line ell. A circle of radius 12 is tangent to line l and is ext…
AMC 10 2024A #15 8학년부터 number-theory, algebra
Let M be the greatest integer such that both M+1213 and M+3773 are perfect squares. What is the units digit of M?
AMC 10 2024A #16 8학년부터 geometry-2d, algebra
All of the rectangles in the figure below, which is drawn to scale, are similar to the enclosing rectangle. Each number…
AMC 10 2024A #17 8학년부터 probability, algebra
Two teams are in a best-two-out-of-three playoff: the teams will play at most 3 games, and the winner of the playoff is…
AMC 10 2024A #18 8학년부터 number-theory
There are exactly K positive integers b with 5 ≤ b ≤ 2024 such that the base-b integer 2024_b is divisible by 16 (where…
AMC 10 2024A #19 6학년부터 algebra, number-theory
The first three terms of a geometric sequence are the integers a, 720, and b, where a<720<b. What is the sum of the digi…
AMC 10 2024A #20 6학년부터 counting, number-theory
Let S be a subset of {1, 2, 3, …, 2024} such that the following two conditions hold: If x and y are distinct elements of…
AMC 10 2024A #21 8학년부터 algebra
The numbers, in order, of each row and the numbers, in order, of each column of a 5 × 5 array of integers form an arithm…
AMC 10 2024A #22 8학년부터 geometry-2d
Let K be the kite formed by joining two right triangles with legs 1 and √3 along a common hypotenuse. Eight copies of K…
AMC 10 2024A #23 8학년부터 algebra, number-theory
Integers a, b, and c satisfy ab + c = 100, bc + a = 87, and ca + b = 60. What is ab + bc + ca?
AMC 10 2024A #24 7학년부터 probability, geometry-3d, counting
A bee is moving in three-dimensional space. A fair six-sided die with faces labeled A⁺, A⁻, B⁺, B⁻, C⁺, and C⁻ is rolled…
AMC 10 2024A #25 7학년부터 counting, geometry-2d
The figure below shows a dotted grid 8 cells wide and 3 cells tall consisting of 1''×1'' squares. Carl places 1-inch too…

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