Difference between revisions of "2014 AMC 12A Problems"
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==Problem 9== | ==Problem 9== | ||
| + | Five positive consecutive integers starting with <math>a</math> have average <math>b</math>. What is the average of <math>5</math> consecutive integers that start with <math>b</math>? | ||
| + | |||
| + | <math> \textbf{(A)}\ a+3\qquad\textbf{(B)}\ a+4\qquad\textbf{(C)}\ a+5\qquad\textbf{(D)}}\ a+6\qquad\textbf{(E)}\ a+7</math> | ||
==Problem 10== | ==Problem 10== | ||
Revision as of 10:42, 7 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
What is 
$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ \frac{25}{2}\qquad\textbf{(D)}}\ \frac{170}{3}\qquad\textbf{(E)}\ 170$ (Error compiling LaTeX. Unknown error_msg)
Problem 2
At the theater children get in for half price. The price for 
adult tickets and 
child tickets is 
. How much would 
adult tickets and 
child tickets cost?
Problem 3
Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible?
$\textbf{(A)}\ 2\qquad\textbf{(B)}\ 3\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}}\ 5\qquad\textbf{(E)}\ 6$ (Error compiling LaTeX. Unknown error_msg)
Problem 4
Suppose that 
cows give 
gallons of milk in 
days. At this rate, how many gallons of milk will 
cows give in 
days?
$\textbf{(A)}\ \frac{bde}{ac}\qquad\textbf{(B)}\ \frac{ac}{bde}\qquad\textbf{(C)}\ \frac{abde}{c}\qquad\textbf{(D)}}\ \frac{bcde}{a}\qquad\textbf{(E)}\ \frac{abc}{de}$ (Error compiling LaTeX. Unknown error_msg)
Problem 5
On an algebra quiz, 
of the students scored 
points, 
scored 
points, 
scored 
points, and the rest scored 
points. What is the difference between the mean and median score of the students' scores on this quiz?
$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}}\ 4\qquad\textbf{(E)}\ 5$ (Error compiling LaTeX. Unknown error_msg)
Problem 6
The difference between a two-digit number and the number obtained by reversing its digits is times the sum of the digits of either number. What is the sum of the two digit number and its reverse?
Problem 7
The first three terms of a geometric progression are 
, ![$\sqrt[3]3$](http://latex.artofproblemsolving.com/9/d/f/9df2b093dad7aff038bf8e76013debc0f33465dc.png)
, and ![$\sqrt[6]3$](http://latex.artofproblemsolving.com/f/7/6/f76bf02aeb1d529aef2a4953c053ddaef97334fb.png)
. What is the fourth term?
![$\textbf{(A) }1\qquad \textbf{(B) }\sqrt[7]3\qquad \textbf{(C) }\sqrt[8]3\qquad \textbf{(D) }\sqrt[9]3\qquad \textbf{(E) }\sqrt[10]3\qquad$](http://latex.artofproblemsolving.com/e/1/8/e186a4e2e8aeaae448bf32163d0887f495e72c5a.png)
Problem 8
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon 1: off the listed price if the listed price is at least 
Coupon 2: 
dollars off the listed price if the listed price is at least
Coupon 3: 
off the amount by which the listed price exceeds
For which of the following listed prices will coupon 
offer a greater price reduction than either coupon 
or coupon 
?
Problem 9
Five positive consecutive integers starting with have average . What is the average of consecutive integers that start with ?
$\textbf{(A)}\ a+3\qquad\textbf{(B)}\ a+4\qquad\textbf{(C)}\ a+5\qquad\textbf{(D)}}\ a+6\qquad\textbf{(E)}\ a+7$ (Error compiling LaTeX. Unknown error_msg)
