경시 · AMC 대비 · 4단계 중 4

AMC 10 2017B 문제 25개

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

AMC 10 2017B #1 3학년부터 arithmetic
Mary thought of a positive two-digit number. She multiplied it by 3 and added 11. Then she switched the digits of the re…
AMC 10 2017B #2 6학년부터 rate-ratio
Sofia ran 5 laps around the 400-meter track at her school. For each lap, she ran the first 100 meters at an average spee…
AMC 10 2017B #3 7학년부터 algebra
Real numbers x, y, and z satisfy the inequalities 0<x<1, -1<y<0, and 1<z<2. Which of the following numbers is necessaril…
AMC 10 2017B #4 7학년부터 algebra
Supposed that x and y are nonzero real numbers such that (3x+y)/(x-3y)=-2. What is the value of (x+3y)/(3x-y)?
AMC 10 2017B #5 7학년부터 arithmetic
Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now has…
AMC 10 2017B #6 5학년부터 arithmetic
What is the largest number of solid 2-in × 2-in × 1-in blocks that can fit in a 3-in × 2-in×3-in box?
AMC 10 2017B #7 7학년부터 rate-ratio
Samia set off on her bicycle to visit her friend, traveling at an average speed of 17 kilometers per hour. When she had…
AMC 10 2017B #8 8학년부터 geometry-2d
Points A(11, 9) and B(2, -3) are vertices of △ ABC with AB=AC. The altitude from A meets the opposite side at D(-1, 3).…
AMC 10 2017B #9 7학년부터 probability
A radio program has a quiz consisting of 3 multiple-choice questions, each with 3 choices. A contestant wins if he or sh…
AMC 10 2017B #10 8학년부터 arithmetic
The lines with equations ax-2y=c and 2x+by=-c are perpendicular and intersect at (1, -5). What is c?
AMC 10 2017B #11 7학년부터 rate-ratio
At Typico High School, 60% of the students like dancing, and the rest dislike it. Of those who like dancing, 80% say tha…
AMC 10 2017B #12 7학년부터 rate-ratio
Elmer's new car gives 50% percent better fuel efficiency, measured in kilometers per liter, than his old car. However, h…
AMC 10 2017B #13 6학년부터 arithmetic
There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each stud…
AMC 10 2017B #14 7학년부터 probability
An integer N is selected at random in the range 1≤ N ≤ 2020 . What is the probability that the remainder when N¹⁶ is div…
AMC 10 2017B #15 8학년부터 geometry-2d
Rectangle ABCD has AB=3 and BC=4. Point E is the foot of the perpendicular from B to diagonal AC. What is the area of △…
AMC 10 2017B #16 4학년부터 arithmetic
How many of the base-ten numerals for the positive integers less than or equal to 2017 contain the digit 0?
AMC 10 2017B #17 7학년부터 counting
Call a positive integer monotonous if it is a one-digit number or its digits, when read from left to right, form either…
AMC 10 2017B #18 8학년부터 geometry-2d
In the figure below, 3 of the 6 disks are to be painted blue, 2 are to be painted red, and 1 is to be painted green. Two…
AMC 10 2017B #19 8학년부터 geometry-2d
Let ABC be an equilateral triangle. Extend side AB beyond B to a point B' so that BB'=3 · AB. Similarly, extend side BC…
AMC 10 2017B #20 7학년부터 probability
The number 21!=51,090,942,171,709,440,000 has over 60,000 positive integer divisors. One of them is chosen at random. Wh…
AMC 10 2017B #21 8학년부터 geometry-2d
In △ ABC, AB=6, AC=8, BC=10, and D is the midpoint of BC. What is the sum of the radii of the circles inscribed in △ ADB…
AMC 10 2017B #22 8학년부터 geometry-2d
The diameter AB of a circle of radius 2 is extended to a point D outside the circle so that BD=3. Point E is chosen so t…
AMC 10 2017B #23 6학년부터 number-theory
Let N=123456789101112…4344 be the 79-digit number that is formed by writing the integers from 1 to 44 in order, one afte…
AMC 10 2017B #24 8학년부터 geometry-2d
The vertices of an equilateral triangle lie on the hyperbola xy=1, and a vertex of this hyperbola is the centroid of the…
AMC 10 2017B #25 6학년부터 algebra
Last year Isabella took 7 math tests and received 7 different scores, each an integer between 91 and 100, inclusive. Aft…

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