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Question 1

AMC8 2026 · Q1

What is the value of the following expression? $1+2-3+4+5-6+7+8-9+10+11-12$

以下表达式的值是多少？ $1+2-3+4+5-6+7+8-9+10+11-12$

(A) 18 18 (B) 21 21 (C) 24 24 (D) 27 27 (E) 30 30

Question 2

AMC8 2026 · Q4

Brynn's savings decreased by $20\%$ in July, then increased by $50\%$ in August. Brynn's savings are now what percent of the original amount?

布琳的存款在七月份减少了$20\%$，然后在八月份增加了$50\%$。布琳的存款现在是原来金额的百分之多少？

(A) 80 80 (B) 90 90 (C) 100 100 (D) 110 110 (E) 120 120

Question 3

AMC8 2026 · Q6

Peter lives near a rectangular field that is filled with blackberry bushes. The field is 10 meters long and 8 meters wide, and Peter can reach any blackberries that are within 1 meter of an edge of the field. The portion of the field he can reach is shaded in the figure below. What fraction of the area of the field can Peter reach?

彼得住在一个长方形的田地附近，田地里长满了黑莓灌木。田地长10米，宽8米，彼得可以够得着离田地边缘1米以内的任何黑莓。田地中彼得能够够到的部分在下面的图中阴影部分所示。彼得能够够到的田地面积占田地总面积的几分之几？

(A) \frac{1}{6} \frac{1}{6} (B) \frac{1}{4} \frac{1}{4} (C) \frac{1}{3} \frac{1}{3} (D) \frac{3}{8} \frac{3}{8} (E) \frac{2}{5} \frac{2}{5}

Question 4

AMC8 2026 · Q8

A poll asked a number of people if they liked solving mathematics problems. Exactly $74\%$ answered "yes." What is the fewest possible number of people who could have been asked the question?

一项调查问了若干人他们是否喜欢解数学题。恰好有 $74\%$ 的人回答“喜欢”。被问的最少人数可能是多少？

(A) 10 10 (B) 20 20 (C) 25 25 (D) 50 50 (E) 100 100

Question 5

AMC8 2026 · Q11

Squares of side length $1, 1, 2, 3,$ and $5$ are arranged to form the rectangle shown below. A curve is drawn by inscribing a quarter circle in each square and joining the quarter circles in order, from shortest to longest. What is the length of the curve?

边长分别为 $1, 1, 2, 3$ 和 $5$ 的正方形排列成下图所示的长方形。在每个正方形内都内切一个四分之一圆，并按从最短边到最长边的顺序将这些四分之一圆连接成一条曲线。该曲线的长度是多少？

(A) \ 4\pi \ 4\pi (B) \ 6\pi \ 6\pi (C) \frac{13}{2}\pi \frac{13}{2}\pi (D) \ 8\pi \ 8\pi (E) \ 13\pi \ 13\pi

Question 6

AMC8 2026 · Q14

Jami picked three equally spaced integer numbers on the number line. The sum of the first and the second numbers is 40, while the sum of the second and third numbers is 60. What is the sum of all three numbers?

Jami在线上选择了三个等间距的整数。第一个和第二个数的和是40，而第二个和第三个数的和是60。三个数的总和是多少？

(A) 70 70 (B) 75 75 (C) 80 80 (D) 85 85 (E) 90 90

Question 7

AMC8 2026 · Q16

Consider all positive four-digit integers consisting of only even digits. What fraction of these integers are divisible by $4$?

考虑所有只由偶数组成的正四位数。这些整数中有多少比例是能被 $4$ 整除的？

(A) \frac{1}{4} \frac{1}{4} (B) \frac{2}{5} \frac{2}{5} (C) \frac{1}{2} \frac{1}{2} (D) \frac{3}{5} \frac{3}{5} (E) \frac{3}{4} \frac{3}{4}

Question 8

AMC8 2026 · Q18

In how many ways can $60$ be written as the sum of two or more consecutive odd positive integers that are arranged in increasing order?

有多少种方法可以将 $60$ 写成两个或两个以上递增排列的连续奇正整数的和？

(A) 1 1 (B) 2 2 (C) 3 3 (D) 4 4 (E) 5 5

Question 9

AMC8 2026 · Q22

The integers from 1 through 25 are arbitrarily separated into five groups of 5 numbers each. The median of each group is identified. Let $M$ equal the median of the five medians. What is the least possible value of $M$?

将从 1 到 25 的整数任意分成五组，每组 5 个数。找出每组的中位数。设 $M$ 为这五个中位数的中位数。问 $M$ 的最小可能值是多少？

(A) 9 9 (B) 10 10 (C) 12 12 (D) 13 13 (E) 14 14

Question 10

AMC8 2026 · Q24

The notation $n!$ (read "n factorial") is defined as the product of the first $n$ positive integers. (For example, $3!=1 \cdot 2 \cdot 3 = 6$). Define the superfactorial of a positive integer, denoted by $n^!$, to be the product of the factorials of the first $n$ integers. (For example, $3^!=1! \cdot 2! \cdot 3! = 12$). How many factors of $7$ appear in the prime factorization of $51^!$, the superfactorial of $51$?

符号 $n!$（读作“n 的阶乘”）定义为前 $n$ 个正整数的乘积。（例如，$3! = 1 \cdot 2 \cdot 3 = 6$）。定义正整数的超阶乘，记为 $n^!$，为前 $n$ 个整数的阶乘的乘积。（例如，$3^! = 1! \cdot 2! \cdot 3! = 12$）。$51^!$（51 的超阶乘）在素因数分解中包含多少个因子 7？

(A) 147 147 (B) 150 150 (C) 156 156 (D) 168 168 (E) 171 171

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