1. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

a. 1/8 b. 2/9 c. 2/7

d. 3/8 e. 1/2

1. Answer: d. 3/8

Explanation:To determine the probability that a senior's name will be chosen, you must determine the total number of seniors' names that are in the lottery and divide this number by the total number of names in the lottery. Since each senior's name is placed in the lottery 3 times, there are 3 × 100 = 300 seniors' names. Likewise, there are 2 × 150 = 300 juniors' names and 1 × 200 = 200 sophomores' names in the lottery. The probability that a senior's name will be chosen is 3/8, or 300/800.

Courtesy College Board

NOONTIME TEMPERATURES IN HILO, HAWAIIMon Tue Wed Thu Fri Sat Sun 66 78 75 69 78 77 70

2. The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?

(A) a < m < f (B) a < f < m (C) m < a < f(D) m < f < a (E) a = m < f

Correct Answer: 2. AExplanation:

To determine the correct order of m, ƒ, and a, it is helpful to first place the seven temperatures in ascending order as shown below:

66 69 70 75 77 78 78The median temperature is the middle

temperature in the ordered list, which is 75, so m = 75. The temperature that occurs most often, or the mode, is 78, so f = 78. To determine the average, you can add the seven numbers together and divide by 7. However, you can determine the relationship between the average and the median by inspection. The three numbers greater than 75 are closer to 75 than are the three numbers smaller than 75. Therefore, the average of the seven numbers will be less than 75. The correct order of m, ƒ, and a is a < m < f.

Courtesy College Board

3. If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?

(A) k + 5 (B) k + 15 (C) k + 20

(D) k + 30 (E) k + 45

Correct Answer: 3. DExplanation:Since k is divisible by 2, 3, and 15, k must be a multiple of 30, as 30 is

the least common multiple of 2, 3, and 15. Some multiples of 30 are 0, 30, 60, 90, and 120.

If you add two multiples of 30, the sum will also be a multiple of 30. For example, 60 and 90 are multiples of 30 and their sum, 150, is also a multiple of 30.

If you add a multiple of 30 to a number that is not a multiple of 30, the sum will not be a multiple of 30. For example, 60 is a multiple of 30 and 45 is not. Their sum, 105, is not a multiple of 30.

The question asks which answer choice is divisible by 2, 3, and 15; that is, which answer choice is a multiple of 30. All the answer choices are in the form of "k plus a number." Only choice (D), k + 30, has k added to a multiple of 30. The sum of k and 30 is also a multiple of 30, so the correct answer is choice (D).

Courtesy College Board

4. In a sack of 50 marbles, there are 20 more red marbles than blue marbles. All of the marbles in the sack are either red or blue. How many blue marbles are in the sack?

Answer: 4. 15 blue marbles

Let x = blue marblesLet x + 20 = red marblesx + (x + 20) = 502x + 20 = 502x = 30X = 15

Courtesy Spark Noteshttp://www.sparknotes.com/testprep/books/newsat/chapter19section15.rhtml

5. Jim roller skates 6 miles per hour. One morning, Jim starts roller skating and doesn’t stop until he has gone 60 miles. How many hours did he spend roller skating?

5. Answer: 10 hours

Courtesy SparkNotes

Distance = Rate x Time60 miles = 6 x T60/6 = TT = 10

6. At a cycling race, the cyclist from California can cycle 528,000 feet per hour. If the race is 480 miles long, how long will it take her to finish the race? (1 mile = 5280 feet)

6. Answer:For the cycling question, since the

question tells you that there are 5,280 feet in a mile, you can find the rate for miles per hour:

528,000 feet/hr / 5,280 ft. mile = 100 mph

Now you can plug the information into the rate formula:

Time: x hours cycling Rate: 100 miles per hour Distance: 480 miles480 miles / 100mph = 4.8 hoursCourtesy SparkNotes

http://www.sparknotes.com/testprep/books/newsat/chapter19section16.html

7.   A weight estimator at a fair guesses that a woman weighs 167 lbs. She actually weighs 179. The percent of error in this estimate is?

A. 5 1/4 % B. 6 7/10% C. 11 12/17% D. 10%E. .67%

7. Answer: B.First, subtract the guess

from the actual weight:179-167 = 12 pounds. Now

divide 12 by 179, the actual weight, to get the percentage of error: 12/179 = .067 = 6.7%.

Courtesy SATPrepHelp.com

http://www.satprephelp.com/sat_word_problems.htm

8.   If the outer diameter of a plastic pipe is 4.25 cm, and the inner diameter of a plastic pipe is 3.13 cm, the thickness of the plastic in centimeters is

A. .56 B. 1.12 C. 2.24 D. 2.98 E. 3.13

8. Answer: A. = .56 Picture a plastic pipe seen from the

end: you can see from the drawing that the longer diameter passes through two thicknesses of pipe. Subtract 3.13 from 4.25 and you get 1.12, but that represents two widths of pipe, so you divide 1.12 by 2. You then get .56 cm thickness.

Courtesy SATPrepHelp.comhttp://www.satprephelp.com/sat_word_problems.htm

4.25

3.13

9. After receiving his weekly paycheck on Friday, a man buys a television for $100, a suit for $200, and a radio for $50. If the total money he spent amounts to 40% of his paycheck, what is his weekly salary?

9. Answer: $875

Explanation:$350 represents 4/10 of his

salary. Divide $350 by 4 to find 1/10 of his salary; that equals $87.50. Multiply 1/10 or 87.50 by 10 to get his full salary of $875.

10. Lauren and Abbey are performing science experiments in which each girl starts off with a collection of 6 fruit flies. If Lauren’s species of fruit flies triples its population every four days and Abbey’s species of fruit flies doubles its population every three days, how many fruit flies will they have if they combine their collections at the end of 12 days?

a. 96 b. 162 c. 192

d. 258 e. 324

10. Answer: D. -- 258

6 x 3 = 18 x 3 = 54 x 3 = 162 for Lauren6 x 2 = 12 x 2 = 24 x 2 = 48 x 2 = 96 for

Abbey96 + 162 = 258

Hint: Watch out for partial answers. Notice that the distractors 162 and 96 are both listed as possible answer choices; however the question asks you the total if they combine their collections.

Courtesy Cracking the PSAT: Princeton Review (p. 25)

11. On Tuesday, Martha does ½ of her weekly homework. On Wednesday, she does 1/3 of the remaining homework. After Wednesday, what fractional part of her homework remains to be done?

a. 1/6 b. 1/5 c. ¼d. 1/3 e. 1/2

11. Answer: D. – 1/3Explanation:Convert all parts to sixths.

Martha does 3/6 the first day and 1/3 x (of) the remaining 3/6 the second day, or 1/6. Now she’s completed 3/6 + 1/6, so she’s done 4/6, or 2/3 of the work. She has 2/6 or 1/3 left.

Courtesy Cracking the PSAT: Princeton Review (p. 110)

12. Seven students in Mrs. Long’s English class scored 91, 83, 92, 83, 91, 85, and 91 on their final exams. What is the mode of her students’ scores?

12. Answer: 91

Explanation:Mode means the number

that occurs most frequently. Since there were three 91’s, that is the mode.

13. In a certain bag of marbles, the ratio of red marbles to green marbles is 7:5. If the bag contains 96 marbles, how many green marbles are in the bag?

13. Answer: 40Explanation:If the ratio is 7:5, there are twelve

“parts” or groups of marbles in the bag. Divide 96 by 12 to find out how many marbles are in one part (group). That division shows that there are 8 marbles in a group. Since green represents 5 groups, that’s 40 marbles.

Courtesy Princeton Review: Cracking the PSAT (p. 127)

14.At the school cafeteria, students can choose from 3 different salads and 5 different main dishes. They can also choose from 2 desserts. If Isabel chooses one salad, one main dish, and one dessert for lunch, how many different lunches could she choose?

a. 15 b. 30 c. 45d. 60 e. 80

14. Answer: b. 30

Explanation: The number of possible combinations is the product of the number of things that Isabel can choose from: in this case, 3 different salads x 5 different main dishes x 2 different dessert options = 30 possible combinations.

Courtesy Princeton Review: Cracking the PSAT

(p. 159)

15. Jennifer wants to visit 4 different cities on her vacation. If she will visit them one at a time, in how many different orders can she see the four cities?

a. 4 b. 16 c. 24

d. 30 e. 36

15. Answer: c. 24Explanation: Draw four blanks to

represent the four cities Jennifer can visit: ___ ___ ______.

Initially she has 4 choices of which city to visit first, then 3 choices, then 2 choices, and finally, 1 choice: 4 x 3 x 2 x 1 = 24. Those are the possible combinations she could come up with.

Courtesy Princeton Review: Cracking the PSAT (p. 160)