Difference between revisions of "2025 AMC 10B Problems"

Latest revision as of 17:46, 3 November 2025

2025 AMC 10B (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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2025 AMC 10B (Problems • Answer Key • Resources)
Preceded by 2025 AMC 10A Problems	Followed by 2026 AMC 10A Problems
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All AMC 10 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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 ==Problem 1==
-Cities <math>A</math> and <math>B</math> are <math>45</math> miles apart. Alicia lives in <math>A</math> and Beth lives in <math>B</math>. Alicia bikes towards <math>B</math> at 18 miles per hour. Leaving at the same time, Beth bikes toward <math>A</math> at 12 miles per hour. How many miles from City <math>A</math> will they be when they meet?
-<math>\textbf{(A) }20\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27</math>
 ==Problem 2==
-The weight of <math>\frac{1}{3}</math> of a large pizza together with <math>3 \frac{1}{2}</math> cups of orange slices is the same weight of <math>\frac{3}{4}</math> of a large pizza together with <math>\frac{1}{2}</math> cups of orange slices. A cup of orange slices weigh <math>\frac{1}{4}</math> of a pound. What is the weight, in pounds, of a large pizza?
-<math>\textbf{(A) }1\frac{4}{5}\qquad\textbf{(B) }2\qquad\textbf{(C) }2\frac{2}{5}\qquad\textbf{(D) }3\qquad\textbf{(E) }3\frac{3}{5}</math>
 ==Problem 3==
-How many positive perfect squares less than <math>2023</math> are divisible by <math>5</math>?
-<math>\textbf{(A) }8\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }11\qquad\textbf{(E) }12</math>
 ==Problem 4==
-How many digits are in the base-ten representation of <math>8^5 \cdot 5^{10} \cdot 15^5</math>?
-<math>\textbf{(A)}~14\qquad\textbf{(B)}~15\qquad\textbf{(C)}~16\qquad\textbf{(D)}~17\qquad\textbf{(E)}~18\qquad</math>
 ==Problem 5==
-Janet rolls a standard <math>6</math>-sided die <math>4</math> times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal <math>3?</math>
-<math>\textbf{(A) }\frac{2}{9}\qquad\textbf{(B) }\frac{49}{216}\qquad\textbf{(C) }\frac{25}{108}\qquad\textbf{(D) }\frac{17}{72}\qquad\textbf{(E) }\frac{13}{54}</math>
 ==Problem 6==
-Points <math>A</math> and <math>B</math> lie on the graph of <math>y=\log_{2}x</math>. The midpoint of <math>\overline{AB}</math> is <math>(6, 2)</math>. What is the positive difference between the <math>x</math>-coordinates of <math>A</math> and <math>B</math>?
-<math>\textbf{(A)}~2\sqrt{11}\qquad\textbf{(B)}~4\sqrt{3}\qquad\textbf{(C)}~8\qquad\textbf{(D)}~4\sqrt{5}\qquad\textbf{(E)}~9</math>
 ==Problem 7==
-A digital display shows the current date as an <math>8</math>-digit integer consisting of a <math>4</math>-digit year, followed by a <math>2</math>-digit month, followed by a <math>2</math>-digit date within the month. For example, Arbor Day this year is displayed as <math>20230428</math>. For how many dates in <math>2023</math> will each digit appear an even number of times in the 8-digital display for that date?
-<math>\textbf{(A)}~5\qquad\textbf{(B)}~6\qquad\textbf{(C)}~7\qquad\textbf{(D)}~8\qquad\textbf{(E)}~9</math>
 ==Problem 8==

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Difference between revisions of "2025 AMC 10B Problems"

Latest revision as of 17:46, 3 November 2025

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