Sample Question 1

Out of a group of drivers surveyed, 15 drove a truck, 22 drove a car, and 9 drove a motorcycle. 10 are both truck and car enthusiasts, 5 enjoy both car and motorcycles and 8 like both trucks and motorcycles. 4 like all 3 vehicles. How many in the group like either trucks or cars or motorcycles?

A. 27
B. 33
C. 42
D. 56

The answer is A, 27. In this case, it helps to draw a Venn diagram.

From this diagram we can see we have the following:

n(T) = 15, n(C) = 22, n(M) = 9, n(T ∩ C) = 10, n(C ∩ M) = 5, n(T ∩ M) = 8, n(T ∩ C ∩ M) = 4

The number of people surveyed that only like trucks = 1
The number of people surveyed that only like cars = 11
The number of people surveyed that only like motorcycles = 0

So the number of people who who like either trucks, cars or motorcycles is: 1 + 11 + 0 + 6 + 4 + 1 + 4 = 27

Sample Question 2

What is the probability of a 2, 4 or 6 showing if two dice are rolled?

A. 1/2
B. 2/3
C. 3/4
D. 5/7

The answer is C, 3/4. The general addition rule needs to be applied here. That is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

This says that the probability that a 2, 4 or 6 showing if two dice are rolled by adding the favorable outcomes and subtracting the probability of both occuring.
The probability of a 2, 4 or 6 showing on one die is 1/2
P(A) = 1/2, P(B) = 1/2, and P(A ∩ B) = 1/4

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 1/2 + 1/2 - 1/4
= 3/4

Sample Question 3

Does the following relation represent a function?

A. Yes
B. No

The answer is A, Yes, the relation is a function. You can determine if a relation is a function by giving it the vertical line test. if there is no single point where the vertical line touches the relation twice, it is a relation.

Sample Question 4

A cabin is 20 feet wider than it is long. If the cabin has a total of 525 square feet, what is the perimeter?

A. 1380
B. 1440
C. 1820
D. 2010

The answer is B, 1440. Since the cabin is 20 feet wider than it is long, let x + 20 be the width and x be the length.

Area is length * width or (x + 20)(x).
x² + 20x = 525
x² + 20x - 525 = 0
(x + 35)(x - 15) = 0 (Result from finding what two numbers added equal 20 and what two numbers multiplied equal -525)
x = 35. (Negative 15 is rejected since it can't be used to calculate our perimeter.)

Perimeter = x + x + (20+x) + (20+x)
40 + 4x = 40 + 4(35) = 1440

Sample Question 5

Which absolute value inequality below represents this graph?

A. |x| ≤ 4
B. |x| ≥ 4
C. |x| < 4
D. |x| > 4

The answer is C, |x| < 4. The unfilled circles represent -4 < x < 4. Calculating the following gives us:

|x| < 4
-4 < x < 4