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2007 AMC 12B Problems

Revision as of 19:51, 9 November 2007 by Minsoens (talk | contribs) (→‎Problem 3)

Problem 1

Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?

$\mathrm {(A)} 678$ $\mathrm {(B)} 768$ $\mathrm {(C)} 786$ $\mathrm {(D)} 867$ $\mathrm {(E)} 876$


Solution

Problem 2

A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his parents' SUV and averaged only 20 miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?

$\mathrm {(A)} 22$ $\mathrm {(B)} 24$ $\mathrm {(C)} 25$ $\mathrm {(D)} 26$ $\mathrm {(E)} 28$


Solution

Problem 3

The point $O$ is the center of the circle circumscribed about triangle $ABC$, with $\angle BOC = 120^{\circ}$ and $\angle AOB = 140^{\circ}$, as shown. What is the degree measure of $\angle ABC$?

2007 12B AMC-3.png

$\mathrm {(A)} 35$ $\mathrm {(B)} 40$ $\mathrm {(C)} 45$ $\mathrm {(D)} 50$ $\mathrm {(E)} 60$


Solution

Problem 4

At Frank's Fruit Market, 3 bananas cost as much as 2 apples, and 6 apples cost as much as 4 oranges. How many oranges cost as much as 18 bananas?

$\mathrm {(A)} 6$ $\mathrm {(B)} 8$ $\mathrm {(C)} 9$ $\mathrm {(D)} 12$ $\mathrm {(E)} 18$


Solution

Problem 5

The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each problem left unanswered. After looking over the 25 problems, Sarah has decided to attempt the first 22 and leave the last 3 unanswered. How many of the first 22 problems must she solve correctly in order to score at least 100 points?

$\mathrm {(A)} 13$ $\mathrm {(B)} 14$ $\mathrm {(C)} 15$ $\mathrm {(D)} 16$ $\mathrm {(E)} 17$


Solution

Problem 6

Triangle $ABC$ has side lengths $AB = 5$, $BC = 6$, and $AC = 7$. Two bugs start simultaneously from $A$ and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point $D$. What is $BD$?

$\mathrm {(A)} 1$ $\mathrm {(B)} 2$ $\mathrm {(C)} 3$ $\mathrm {(D)} 4$ $\mathrm {(E)} 5$

Solution

Problem 7

All sides of the convex pentagon $ABCDE$ are of equal length, and $\angle A = \angle B = 90^{\circ}$. What is the degree measure of $\angle E$?

$\mathrm {(A)} 90$ $\mathrm {(B)} 108$ $\mathrm {(C)} 120$ $\mathrm {(D)} 144$ $\mathrm {(E)} 150$


Solution

Problem 8

Tom's age is $T$ years, which is also the sum of the ages of his three children. His age $N$ years ago was twice the sum of their ages then. What is $T/N$ ?

$\mathrm {(A)} 2$ $\mathrm {(B)} 3$ $\mathrm {(C)} 4$ $\mathrm {(D)} 5$ $\mathrm {(E)} 6$


Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

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