2017 AMC 10B Problems
2017 AMC 10B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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Problem 1
Mary thought of a positive two-digit number. She multiplied it by and added
. Then she switched the digits of the result, obtaining a number between
and
, inclusive. What was Mary's number?
Problem 2
Sofia ran laps around the
-meter track at her school. For each lap, she ran the first
meters at an average speed of
meters per second and the remaining
meters at an average speed of
meters per second. How much time did Sofia take running the
laps?
minutes and
seconds
minutes and
seconds
minutes and
seconds
minutes and
seconds
minutes and
seconds
Problem 22
The diameter of a circle of radius
is extended to a point
outside the circle so that
. Point
is chosen so that
and line
is perpendicular to line
. Segment
intersects the circle at a point
between
and
. What is the area of
?
Problem 23
Let be the
-digit number that is formed by writing the integers from
to
in order, one after the other. What is the remainder when
is divided by
?
Problem 24
The vertices of an equilateral triangle lie on the hyperbola , and a vertex of this hyperbola is the centroid of the triangle. What is the square of the area of the triangle?
Problem 25
Last year Isabella took math tests and received
different scores, each an integer between
and
, inclusive. After each test she noticed that the average of her test scores was an integer. Her score on the seventh test was
. What was her score on the sixth test?