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, HAWAII
Mon 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 oneweek 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. A
Explanation:
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 78
The 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. D
Explanation:
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 marbles
Let x + 20 = red marbles
x + (x + 20) = 50
2x + 20 = 50
2x = 30
X = 15
Courtesy Spark Notes
http://www.sparknotes.com/testprep/books/newsat/c
hapter19section15.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 Time
60 miles = 6 x T
60/6 = T
T = 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 miles
480 miles / 100mph = 4.8 hours
Courtesy 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.com
http://www.satprephelp.com/sat_word_problems.
htm
3.13
4.25
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 Lauren
6 x 2 = 12 x 2 = 24 x 2 = 48 x 2 = 96 for Abbey
96 + 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.
d.
1/6
1/3
b. 1/5
e. 1/2
c. ¼
11. Answer: D. – 1/3
Explanation:
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: 40
Explanation:
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. 45
d. 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. 24
Explanation: 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)