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==Problem 4 ==
 
==Problem 4 ==

Revision as of 13:44, 17 November 2022

2022 AMC 10B (Answer Key)
Printable versions: Wiki • AoPS Resources • PDF

Instructions

  1. 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.
  2. 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.
  3. 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).
  4. Figures are not necessarily drawn to scale.
  5. You will have 75 minutes working time to complete the test.
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Problem 1

XXX

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

Solution

Problem 2

XXX

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

Solution

Problem 3

XXX

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

Solution

Problem 4

A donkey suffers an attack of hiccups and the first hiccup happens at $\text{4:00}$ one afternoon. Suppose that the donkey hiccups regularly every $5$ seconds. At what time does the donkey’s $\text{700th}$ hiccup occur?

$\textbf{(A) }$ $15$ seconds after $\text{4:58}$

$\textbf{(B) }$ $20$ seconds after $\text{4:58}$

$\textbf{(C)}$ $25$ seconds after $\text{4:58}$

$\textbf{(D) }$ $30$ seconds after $\text{4:58}$

$\textbf{(E) }$ $35$ seconds after $\text{4:58}$

Solution

Problem 5

XXX

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

Solution

Problem 6

How many of the first ten numbers of the sequence $121, 11211, 1112111, \cdots$ are prime numbers?

$\textbf{(A) } 0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }4$

Solution

Problem 7

XXX

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

Solution

Problem 8

XXX

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

Solution

Problem 9

XXX

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

Solution

Problem 10

XXX

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

Solution

Problem 11

XXX

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

Solution

Problem 12

A pair of fair $6$-sided dice is rolled $n$ times. What is the least value of $n$ such that the probability that the sum of the numbers face up on a roll equals $7$ at least once is greater than $\frac{1}{2}$?

$\textbf{(A) } 2 \qquad \textbf{(B) } 3 \qquad \textbf{(C) } 4 \qquad \textbf{(D) } 5 \qquad \textbf{(E) } 6$

Solution

Problem 13

XXX

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

Solution

Problem 14

XXX

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

Solution

Problem 15

XXX

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

Solution

Problem 16

XXX

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

Solution

Problem 17

XXX

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

Solution

Problem 18

XXX

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

Solution

Problem 19

XXX

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

Solution

Problem 20

XXX

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

Solution

Problem 21

XXX

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

Solution

Problem 22

Let $S$ be the set of circles in the coordinate plane that are tangent to each of the three circles with equations $x^{2}+y^{2}=4$, $x^{2}+y^{2}=64$, and $(x-5)^{2}+y^{2}=3$. What is the sum of the areas of all circles in $S$?

$\textbf{(A)}~48\pi\qquad\textbf{(B)}~68\pi\qquad\textbf{(C)}~96\pi\qquad\textbf{(D)}~102\pi\qquad\textbf{(E)}~136\pi\qquad$

Solution

Problem 23

XXX

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

Solution

Problem 24

XXX

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

Solution

Problem 25

XXX

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

Solution

See also

2022 AMC 10B (Problems • Answer Key • Resources)
Preceded by
2021 Fall AMC 10B Problems 		Followed by
2023 AMC 10B Problems
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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