Question

For the game show Who Wants To Be a Millionaire?, the dollar values of each question are shown in the following table (where $\text{K}$ = 1000). $\begin{array}{ccccc} \text{Question} & 1 & 2 & 3 \\ \text{Value} & 100 & 200 & 300 \end{array}$ $\begin{array}{cccccc} 4 & 5 & 6 & 7 & 8 \\ 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} \end{array}$ $\begin{array}{ccccc} 9 & 10 & 11 & 12 \\ 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} \end{array}$ $\begin{array}{ccc} 13 & 14 & 15 \\ 250\text{K} & 500\text{K} & 1000\text{K} \end{array}$ Between which two questions is the percent increase of the value the smallest?

From $1$ to $2$

From $2$ to $3$

From $3$ to $4$

From $11$ to $12$

From $14$ to $15$

Solution:

Most of the listed increases are doublings, which are $100\%$ increases.

The exceptions among the answer choices are from $2$ to $3$ , from $3$ to $4$ , and from $11$ to $12$ .

These percent increases are $\dfrac{300-200}{200}=50\%$ , $\dfrac{500-300}{300}=66\dfrac23\%$ , and $\dfrac{125000-64000}{64000}$ , which is about $95\%$ .

The smallest is from question $2$ to question $3$ .

Thus, B is the correct answer.

2001 AMC 8 Problem 17

Solution:

Problem 17 in Other Years