Difference between revisions of "2014 AMC 10B Problems"
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==Problem 14==  ==Problem 14==  
−  +  Danica drove her new car on a trip for a whole number of hours, averaging <math>55</math> miles per hour. At the beginning of the trip, <math>abc</math> miles was displayed on the odometer, where <math>abc</math> is a 3digit number with <math>a \ge 1</math> and <math>a + b + c \ge 7</math>. At the end of the trip, the odometer showed <math>cba</math> miles. What is <math>a^2 + b^2 + c^2</math> ?  
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+  <math> \textbf {(A) } 26 \qquad \textbf {(B) } 27 \qquad \textbf {(C) } 36 \qquad \textbf {(D) } 37 \qquad \textbf {(E) }41</math>  
==Problem 15==  ==Problem 15==  
Revision as of 13:28, 20 February 2014
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 onefifth 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 A is $x%$ (Error compiling LaTeX. ! Missing $ inserted.) 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
Problem 10
Problem 11
Problem 12
The largest divisor of 2,014,000,000 is itself. What is the fifthlargest 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 3digit number with and . At the end of the trip, the odometer showed miles. What is ?


Problem 15
Problem 16
Four fair sixsided dice are rolled. What is the probability that at least three of the four dice show the same value?
Problem 17
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?