Question

Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of three letters followed by three digits. By how many times is the number of possible license plates increased?

$\dfrac{26}{10}$

$\dfrac{26^2}{10^2}$

$\dfrac{26^2}{10}$

$\dfrac{26^3}{10^3}$

$\dfrac{26^3}{10^2}$

Answer: C

Concepts:multiplication principle ratio and proportion

Difficulty rating: 1170

Solution:

The old scheme allows $26 \cdot 10^4$ plates and the new scheme allows $26^3 \cdot 10^3$ plates. The increase factor is $\dfrac{26^3 \cdot 10^3}{26 \cdot 10^4}=\dfrac{26^2}{10}.$

Thus, the correct answer is C.

2003 AMC 10B Problem 10

Answer: C

Difficulty rating: 1170

Solution:

Problem 10 in Other Years