2005 AMC 12B Problems

This is an empty template page which needs to be filled. You can help us out by finding the needed content and editing it in. Thanks.

Problem 1

Two is $10\%$ of $x$ and $20\%$ of $y$ . What is $x-y$ ?

$\mathrm{(A)}\ 1 \qquad \mathrm{(B)}\ 2 \qquad \mathrm{(C)}\ 5 \qquad \mathrm{(D)}\ 10 \qquad \mathrm{(E)}\ 20$

Solution

Problem 2

The equations $2x+7=3$ and $bx-10=-2$ have the same solution for $x$ . What is the value of $b$ ?

$\mathrm{(A)}\ -8 \qquad \mathrm{(B)}\ -4 \qquad \mathrm{(C)}\ -2 \qquad \mathrm{(D)}\ 4 \qquad \mathrm{(E)}\ 8$

Solution

Problem 3

A rectangle with a diagonal of length $x$ is twice as long as it is wide. What is the area of the rectangle?

$\mathrm{(A)}\ \frac14x^2 \qquad \mathrm{(B)}\ \frac25x^2 \qquad \mathrm{(C)}\ \frac12x^2 \qquad \mathrm{(D)}\ x^2 \qquad \mathrm{(E)}\ \frac32x^2$

Solution

Problem 4

The average (mean) of $20$ numbers is $30, and the average of$ 30 $other numbers is$ 20 $. What is the average of$ \mathrm{(A)}\ \frac14x^2 \qquad \mathrm{(B)}\ \frac25x^2 \qquad \mathrm{(C)}\ \frac12x^2 \qquad \mathrm{(D)}\ x^2 \qquad \mathrm{(E)}\ \frac32x^2 $