2001 AMC 8 Problems/Problem 17: Difference between revisions
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Notice that in two of the increases, the dollar amount doubles. The increases in which this is not true is <math> 2 </math> to <math> 3 </math>, <math> 3 </math> to <math> 4 </math>, and <math> 11 </math> to <math> 12 </math>. We can disregard <math> 11 </math> to <math> 12 </math> since that increase is almost <math> 2 </math> times. The increase from <math> 2 </math> to <math> 3 </math> is <math> \frac{300-200}{200}=\frac{1}{2} </math>, so it's only multiplied by a factor of <math> 1.5 </math>. The increase from <math> 3 </math> to <math> 4 </math> is <math> \frac{500-300}{300}=\frac{2}{3} </math>, so it's only multiplied by a factor of <math> 1.\bar{6} </math>. Therefore, the smallest percent increase is <math> \text{From 2 to 3}, \boxed{\text{B}} </math> | Notice that in two of the increases, the dollar amount doubles. The increases in which this is not true is <math> 2 </math> to <math> 3 </math>, <math> 3 </math> to <math> 4 </math>, and <math> 11 </math> to <math> 12 </math>. We can disregard <math> 11 </math> to <math> 12 </math> since that increase is almost <math> 2 </math> times. The increase from <math> 2 </math> to <math> 3 </math> is <math> \frac{300-200}{200}=\frac{1}{2} </math>, so it's only multiplied by a factor of <math> 1.5 </math>. The increase from <math> 3 </math> to <math> 4 </math> is <math> \frac{500-300}{300}=\frac{2}{3} </math>, so it's only multiplied by a factor of <math> 1.\bar{6} </math>. Therefore, the smallest percent increase is <math> \text{From 2 to 3}, \boxed{\text{B}} </math> | ||
==Video Solution== | |||
https://youtu.be/S8hyVeObqUs Soo, DRMS, NM | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2001|num-b=16|num-a=18}} | {{AMC8 box|year=2001|num-b=16|num-a=18}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 01:21, 4 March 2022
Problem
For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the following table (where K = 1000).
![\[\begin{tabular}{rccccccccccccccc} \text{Question} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \text{Value} & 100 & 200 & 300 & 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} & 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} & 250\text{K} & 500\text{K} & 1000\text{K} \end{tabular}\]](http://latex.artofproblemsolving.com/f/7/2/f72d71240cdafc0531cc3a8916a28cacd345acdf.png)
Between which two questions is the percent increase of the value the smallest?
Solution
Notice that in two of the increases, the dollar amount doubles. The increases in which this is not true is 
to 
, to 
, and 
to 
. We can disregard to since that increase is almost times. The increase from to is 
, so it's only multiplied by a factor of 
. The increase from to is 
, so it's only multiplied by a factor of 
. Therefore, the smallest percent increase is 
Video Solution
https://youtu.be/S8hyVeObqUs Soo, DRMS, NM
See Also
| 2001 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
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