Difference between revisions of "2014 AMC 10B Problems/Problem 11"
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(3) a <math>25\%</math> discount followed by a <math>5\%</math> discount | (3) a <math>25\%</math> discount followed by a <math>5\%</math> discount | ||
| − | What is the possible positive integer value of <math>n</math>? | + | What is the smallest possible positive integer value of <math>n</math>? |
<math> \textbf{(A)}\ \ 27\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 29\qquad\textbf{(D)}}\ 31\qquad\textbf{(E)}\ 33 </math> | <math> \textbf{(A)}\ \ 27\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 29\qquad\textbf{(D)}}\ 31\qquad\textbf{(E)}\ 33 </math> | ||
Revision as of 17:17, 1 September 2014
Problem
For the consumer, a single discount of 
is more advantageous than any of the following discounts:
(1) two successive 
discounts
(2) three successive 
discounts
(3) a 
discount followed by a 
discount
What is the smallest possible positive integer value of 
?
$\textbf{(A)}\ \ 27\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 29\qquad\textbf{(D)}}\ 31\qquad\textbf{(E)}\ 33$ (Error compiling LaTeX. Unknown error_msg)
Solution
Let the original price be 
. Then, for option 
, the discounted price is 
. For option 
, the discounted price is 
. Finally, for option 
, the discounted price is 
. Therefore, must be greater than 
. It follows must be greater than 
. We multiply this by 
to get the percent value, and then round up because is the smallest integer that provides a greater discount than 
, leaving us with the answer of 
See Also
| 2014 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
