Difference between revisions of "2016 AMC 8 Problems"
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==Problem 21== | ==Problem 21== | ||
− | + | A box contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn? | |
<math>\textbf{(A) }\dfrac{3}{10}\qquad\textbf{(B) }\dfrac{2}{5}\qquad\textbf{(C) }\dfrac{1}{2}\qquad\textbf{(D) }\dfrac{3}{5}\qquad \textbf{(E) }\dfrac{7}{10}</math> | <math>\textbf{(A) }\dfrac{3}{10}\qquad\textbf{(B) }\dfrac{2}{5}\qquad\textbf{(C) }\dfrac{1}{2}\qquad\textbf{(D) }\dfrac{3}{5}\qquad \textbf{(E) }\dfrac{7}{10}</math> |
Revision as of 10:47, 23 November 2016
Contents
Problem 1
The longest professional tennis match ever played lasted a total of hours and minutes. How many minutes was this?
Problem 2
In rectangle , and . Point is the midpoint of . What is the area of ?
Problem 3
Four students take an exam. Three of their scores are and . If the average of their four scores is , then what is the remaining score?
Problem 4
When Cheenu was a boy he could run miles in hours and minutes. As an old man he can now walk miles in hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?
Problem 5
The number is a two-digit number.
• When is divided by , the remainder is .
• When is divided by , the remainder is .
What is the remainder when is divided by ?
Problem 7
Which of the following numbers is not a perfect square?
Problem 8
Find the value of the expression
Problem 9
What is the sum of the distinct prime integer divisors of ?
Problem 10
Suppose that means What is the value of if
Problem 11
Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is
Problem 12
Jefferson Middle School has the same number of boys and girls. Three-fourths of the girls and two-thirds of the boys went on a field trip. What fraction of the students were girls?
Problem 13
Two different numbers are randomly selected from the set and multiplied together. What is the probability that the product is ?
Problem 20
The least common multiple of and is , and the least common multiple of and is . What is the least possible value of the least common multiple of and ?
Problem 21
A box contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?
Problem 22
Rectangle below is a rectangle with . What is the area of the "bat wings" (shaded area)?
Problem 23
Two congruent circles centered at points and each pass through the other circle's center. The line containing both and is extended to intersect the circles at points and . The circles intersect at two points, one of which is . What is the degree measure of ?
Problem 24
The digits , , , , and are each used once to write a five-digit number . The three-digit number is divisible by , the three-digit number is divisible by , and the three-digit number is divisible by . What is ?
Problem 25
A semicircle is inscribed in an isosceles triangle with base and height so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.