2014 AMC 10B Problems
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
Problem 1
Leah has coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth?
Problem 2
What is ?
Problem 3
Randy drove the first third of his trip on a gravel road, the next miles on pavement, and the remaining one-fifth on a dirt road. In miles how long was Randy's trip?
Problem 4
Susie pays for muffins and
bananas. Calvin spends twice as much paying for
muffins and
bananas. A muffin is how many times as expensive as a banana?
Problem 5
Problem 6
Orvin went to the store with just enough money to buy balloons. When he arrived, he discovered that the store had a special sale on balloons: buy
balloon at the regular price and get a second at
off the regular price. What is the greatest number of balloons Orvin could buy?
Problem 7
Suppose and
is
greater than
. What is
?
Problem 8
A truck travels feet ever
seconds. There are
feet in a yard. How many yards does the truck travel in
minutes?
Problem 9
For real numbers and
,
What is
?
$\texbf{(A) } -2014 \qquad\texbf{(B) } \frac{-1}{2014} \qquad\texbf{(C) } \frac{1}{2014} \qquad\texbf{(D) } 1 \qquad\texbf{(E) } 2014$ (Error compiling LaTeX. Unknown error_msg)
Problem 10
Problem 11
Problem 12
The largest divisor of is itself. What is the fifth-largest divisor?
Problem 13
Problem 14
Danica drove her new car on a trip for a whole number of hours, averaging miles per hour. At the beginning of the trip,
miles was displayed on the odometer, where
is a 3-digit number with
and
. At the end of the trip, the odometer showed
miles. What is
?
Problem 15
Problem 16
Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?
Problem 17
What is the greatest power of that is a factor of
?
Problem 18
A list of positive integers has a mean of
, a median of
, and a unique mode of
. What is the largest possible value of an integer in the list?
Problem 19
Two concentric circles have radii and
. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?
Problem 20
For how many integers is the number
negative?
Problem 21
Trapezoid has parallel sides
of length
and
of length
. The other two sides are of lengths
and
. The angles at
and
are acute. What is the length of the shorter diagonal of
?
Problem 22
Problem 23
Problem 24
The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is bad if it is not true that for every from
to
one can find a subset of the numbers that appear consecutively on the circle that sum to
. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?
Problem 25
In a small pond there are eleven lily pads in a row labeled through
. A frog is sitting on pad
. When the frog is on pad
,
, it will jump to pad
with probability
and to pad
with probability
. Each jump is independent of the previous jumps. If the frog reaches pad
it will be eaten by a patiently waiting snake. If the frog reaches pad
it will exit the pond, never to return. what is the probability that the frog will escape being eaten by the snake?