Difference between revisions of "2017 AMC 10B Problems"
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==Problem 6== | ==Problem 6== | ||
− | + | What is the largest number of solid <math>2\text{ in}</math> by <math>2\text{ in}</math> by <math>1\text{ in}</math> blocks that can fit in a <math>3\text{ in}</math> by <math>2\text{ in}</math> by <math>3\text{ in}</math> box? | |
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+ | <math>\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math> | ||
[[2017 AMC 10B Problems/Problem 6|Solution]] | [[2017 AMC 10B Problems/Problem 6|Solution]] |
Revision as of 12:51, 16 February 2017
2017 AMC 10B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
| ||
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 |
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
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 3
Real numbers ,
, and
satify the inequalities
,
, and
.
Which of the following numbers is necessarily positive?
Problem 4
Placeholder
Problem 5
Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?
Problem 6
What is the largest number of solid by
by
blocks that can fit in a
by
by
box?
Problem 7
Placeholder
Problem 8
Placeholder
Problem 9
Placeholder
Problem 10
Placeholder
Problem 11
Placeholder
Problem 12
Placeholder
Problem 13
Placeholder
Problem 14
Placeholder
Problem 15
Placeholder
Problem 16
Placeholder
Problem 17
Placeholder
Problem 18
Placeholder
Problem 19
Placeholder
Problem 20
Placeholder
Problem 21
Placeholder
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?
See also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by 2017 AMC 10A Problems |
Followed by 2018 AMC 10A 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.