GRE Math Review
Solution: To solve, you need to calculate the following two probabilities and then
multiply them
The probability that the rst disk selected from the box will be red
The probability that the second disk selected from the box will be orange,
GRE Math Review
Since B and C are independent, P(B and C) = P(B)P(C). So,
P(B or C) = P(B) + P(C) P(B and C) = P(B) + P(C) P(B)P(C)
Therefore,
P(B or C) = 0.40 + 0.85 (0.40)(0.85) = 1.25 0.34
= 0.91
Example 4.4.5: Suppose that there is a 6-sided die that
GRE Math Review
rolling the die twice, and each outcome is an ordered pair of results like 4
on the rst roll and 1 on the second roll. But event E restricts only the rst
rollto a 3having no effect on the second roll; similarly, event F restricts
only the
GRE Math Review
1
. For any event E, the probability that E occurs, denoted by P(E), is de15
ned by the ratio
equal to
P(E) =
the number of names in the event E
15
7
.
15
In general, for a random experiment with a nite number of possible outcomes, if
each
GRE Math Review
The regions with vertical stripes represent the set A C. The regions with horizontal
stripes represent the set B. The region with both kinds of stripes represents the set
A B. The sets B and C are mutually exclusive, often written B C = .
GRE Math Review
4.
5.
6.
7.
8.
What is the sum of the measures of the interior angles of a decagon (10sided polygon)?
If the decagon in exercise 4 is regular, what is the measure of each interior
angle?
The lengths of two sides of an isosceles triangle ar
GRE Math Review
Bar graphs can also be used to compare different groups using the same categories.
Example 4.1.4:
Enrollment
FALL 2009 AND SPRING 2010 ENROLLMENT
AT THREE COLLEGES
6,000
Fall 2009
Spring 2010
5,000
4,000
3,000
2,000
1,000
0
College A
Colle
GRE Math Review
11.
In parallelogram ABCD below, nd the following.
(a) Area of ABCD
(b) Perimeter of ABCD
(c) Length of diagonal BD
B
C
4
A
12.
12
D
2
The circle with center O below has radius 4. Find the following.
(a) Circumference of the circle
(b) Len
GRE Math Review
14.
For the rectangular solid below, nd the following.
(a) Surface area of the solid
(b) Length of diagonal AB
7
B
2
10
A
ANSWERS TO GEOMETRY EXERCISES
1.
x = 57 and y = 138
2.
x = 70 and y = 125
3.
z=x+y
4.
1,440
5.
144
6.
52 and 59
7.
6
GRE Math Review
Here are the resulting frequency and relative frequency distributions of the data.
Frequency Distribution
Number of
Children
Frequency
0
1
2
3
4
5
3
5
7
6
3
1
Total
25
Relative Frequency Distribution
Number of
Children
Relative
Frequency
0
GRE Math Review
The volume V of a right circular cylinder that has height h and a base with radius r is the product of the height and the area of the base, or
V = pr2h
The surface area A of a right circular cylinder is the sum of the areas of the two
base
GRE Math Review
patterned or systematic way, there are some useful techniques for counting the objects
without actually listing them.
Sets and Lists
The term set has been used informally in this review to mean a collection of objects
that have some proper
GRE Math Review
Example 4.1.2:
FALL 2009 ENROLLMENT AT FIVE COLLEGES
8,000
7,000
Enrollment
6,000
5,000
4,000
3,000
2,000
1,000
0
College A College B College C
College D College E
From the graph, we can conclude that the college with the greatest fall 200
OR
x + 3 = -15
x = -18
so, x - 1 = -19
Only -19 appears in the choices.
12. (B). To evaluate the expression in Quantity A, replace x with 2.
x2 - 4x + 3 =
(2)2 - 4(2) + 3 =
4 - 8 + 3 = -1 < 1
Therefore, Quantity B is greater.
13. (A). To find the value of
b>5
Quantity A
Quantity B
(5b)a
(b2)a
Quantity A
Quantity B
(5 + a)(3 + a)
a2 + 2a + 15
7.
8.
In Triangle ABC, AB = 12, AC = 10, and BC = 5.
9. If
Quantity A
Quantity B
The measure of angle A
The measure of angle C
is a positive integer, how many integer
Quantity A
Quantity B
4.
Quantity A
Quantity B
The slope of line segment AB
The slope of line segment AC
5.
In the figure above, the circle is inscribed a square that has area 16.
Quantity A
Quantity B
The area of the shaded region
1
6.
a>1
5.
Quantity A
Quantity B
17(6) + 3(6)
6(17) + 6(3)
Quantity A
Quantity B
-23/2
(-2)2
Quantity A
Quantity B
53 - 52
5
6.
7.
8.
Quantity A
Quantity B
-10 - (-3)2
- [10 + (-3)2]
Quantity A
Quantity B
(30,000,000)(2,000,000)
(15,000,000)(4,000,000)
9. 32/(4 +
Mr. and Mrs. Gonzales, ages 42 and 39, wish to visit the Natural History Museum with their
three children (ages 4, 6, and 10), and Mr. Gonzaless 69-year-old father.
Quantity A
Quantity B
The cost of admission for
the group on a weekday
The cost of admissi
12. Mitchell plans to work at a day camp over the summer. Each week, he will be paid according to the following
schedule: at the end of the first week, he will receive $1. At the end of each subsequent week, he will receive $1,
plus an additional amount e
Arithmetic Answers
1. (A). First simplify inside the parentheses:
39 - (25 - 17) =
39 - 8 =
31
You could also distribute the minus sign to get 39 - 25 + 17 if you prefer. Quantity B is equal to -3, so the final
answer is (A). If you noticed right away tha
4. If 3x + 7 - 4x + 8 = 2(-2x - 6), what is the value of x?
5. If 2x(4 - 6) = -2x + 12, what is the value of x?
6. If x
0 and
7. If x
-13 and
8. If x
2 and
9. If x
2 and
, what is the value of x?
, what is the value of x?
, what is the value of x?
, what
GRE Quantitative Reasoning
Sample Questions
Select one or more answer choices according to the specic question directions.
If the question does not specify how many answer choices to select, select all
that apply.
The correct answer may be just one of the
GRE Math Review
Every integer greater than 1 either is a prime number or can be uniquely expressed as a product of factors that are prime numbers, or prime divisors. Such an
expression is called a prime factorization. Here are several examples of prime fa
GRE Math Review
Example 2.7.8: If an amount P is to be invested at an annual interest rate of 3.5 percent, compounded annually, what should be the value of P so that the value of the
investment is $1,000 at the end of 3 years?
Solution: According to the f
GRE Quantitative Reasoning Practice Questions
R
Q
P
V
S
T
In the gure above, squares PQRV and VRST have
sides of length 6.
Quantity B
Quantity A
2.
The area of the shaded
region
36
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
In 2009 the property tax on each home in T
GRE Quantitative Reasoning
Here are examples of other standard symbols with their meanings:
xy
xy
xy
x
x
x
n!
m
m
x is less than or equal to y
x and y are not equal
x and y are approximately equal
the absolute value of x
the nonnegative square root of x,
GRE Verbal Reasoning Practice Questions
Questions 3 and 4 are based on the following reading passage.
For hot desert locations with access to seawater, a new greenhouse design generates
freshwater and cool air. Oriented to the prevailing wind, the front w
GRE Quantitative Reasoning
answer and then round the answer to the nearest 10 dollars, as suggested by the
answer choices. The calculator yields the decimal 31.287. . . , which rounds to 30
dollars.
Thus, the correct answer is Choice C, $30.
5.
A certain
GRE Quantitative Reasoning
5.
Convert 6 miles per hour to feet per second.
Explanation
The solution to this problem uses the conversion factors 1 mile = 5,280 feet and
1 hour = 3,600 seconds as follows:
5,280 feet
1 hour
feet
=?
61 miles
hour 1 mile 3,600