单选题
Directions: In the following questions, choose the best answer from the five choices listed.
单选题
Camille's average on her 6 math tests this marking period is 75. Fortunately for Camille, her teacher drops each student's lowest grade, and this raises her average to 85. What was her lowest grade?
【正确答案】
B
【答案解析】On six tests combined, Camille earned a total of 6 × 75 = 450 points [TACTIC El].
The total of her five best grades is 5 × 85 = 425 points, so her lowest grade was 450 -425 = 25.
**Assume that Camille's five best grades were each 85. Then each one has a deviation of 10 points above the average of 75, and the total deviation above 75 is 5 × 10 = 50 points. Therefore, her one bad grade must have been 50 points below 75.
The total of her five best grades is 5 × 85 = 425 points, so her lowest grade was 450 -425 = 25.
**Assume that Camille's five best grades were each 85. Then each one has a deviation of 10 points above the average of 75, and the total deviation above 75 is 5 × 10 = 50 points. Therefore, her one bad grade must have been 50 points below 75.
单选题
What is the surface area in square inches of a cube whose volume is 216 cubic inches?
【正确答案】
C
【答案解析】Since the volume of the cube is 216 cubic inches, we have e3 = 216 [*] e = 6. The area of each face is e2 = 36 square inches, and since there are six faces, the total surface area is 6 × 36 = 216 square inches.
单选题
Last year Leo bought two paintings. This year he sold them for $2000 each. On one, he made a 25% profit, and on the other he had a 25% loss. What was his net loss or profit?
【正确答案】
C
【答案解析】On the first painting, Leo made a 25% profit, so if he bought it for x, he sold it for
x + .25x = 1.25x = 2000 [*]
x = 2000 + 1.25 = 1600.
His profit was $400. On the second painting, Leo lost 25%, so if he bought it for y, he sold it for
y -.25y = .75y = 2000 [*]
y = 2000 + .75 = 2666.67.
His loss was $666.67. In all, he lost $266.67,
which is more than $100.
**In these types of problems you never break even. Eliminate A. When you make a profit,
your purchase price is less than your selling price, and when you incur a loss, your pur-chase price is greater than your selling price.
So the first painting cost less than $2000 and the second cost more than $2000. So Leo earned 25% of a small amount and lost 25% of a large amount. He surely lost money. Eliminate D and E. If you can't solve as above, guess between B and C.
x + .25x = 1.25x = 2000 [*]
x = 2000 + 1.25 = 1600.
His profit was $400. On the second painting, Leo lost 25%, so if he bought it for y, he sold it for
y -.25y = .75y = 2000 [*]
y = 2000 + .75 = 2666.67.
His loss was $666.67. In all, he lost $266.67,
which is more than $100.
**In these types of problems you never break even. Eliminate A. When you make a profit,
your purchase price is less than your selling price, and when you incur a loss, your pur-chase price is greater than your selling price.
So the first painting cost less than $2000 and the second cost more than $2000. So Leo earned 25% of a small amount and lost 25% of a large amount. He surely lost money. Eliminate D and E. If you can't solve as above, guess between B and C.