PCAT Practice: Quantitative Reasoning || with 100%
Errorless Answers.
What is the range of the function below?
f(x) = 3x2- 5
A. (-∞, ∞)
B. (0, ∞)
C. (-5, ∞)
D. (5, ∞) Correct Answer: C
Explanation: The range of a function is the list of possible outputs of the function. It is
impossible for this function to generate any number less than -5, and there is no upper limit to
the output of this function. The range is (-5, ∞).
Which is equivalent to 3i2 + 2i4?
A. -1
B. 1
C. 5
D. 3 + 2i Correct Answer: A
Explanation: This question asks you to manipulate complex numbers. The key to solving this
problem is that i2 = -1. Substitute this into the expression:
3i2+2i4=3i2+2(i2)(i2)=3(−1)+2(−1)(−1)=−3+2=−1
If f(x)=x+25 , then what is f-1(x)?
A. x−2/5
B. 5x- 2
C. 5/x+2
D. 2−x/5 Correct Answer: B
Explanation: If the function is y=f(x)=x+2/5. To find the inverse function, switch x and y and
then solve for y:
x = y+2/5
5x = y+2
y = 5x-2
What is the sum of the two vectors (3 + 2i) and (-2 + i)?
A. 2 + 2i
B. -8
C. -6 + 2i
D. 1 + 3i Correct Answer: D
Explanation: To add vectors, group the real parts together and the imaginary parts together, and
then add:
, (3 + 2i) + (-2 + i) = (3 + -2) + (2i + i) = 1 + 3i
Which of the following is equivalent to (-2 + i)(3 + 2i)?
A. -8 -i
B. 1 + 3i
C. -6 + 2i
D. 5 + 3i Correct Answer: A
Explanation: To multiply two complex numbers, first distribute the parenthesis:
(-2 + i)(3 + 2i) = -6 + 3i- 4i + 2i2 = -6 - i + 2i2.
Then use the fact that i2 = -1:
-6 - i + 2 i2 =-6 - i + 2(-1) = -8 - i.
A candy store has 75 pounds of candy in stock at the beginning of the day. If x is the percentage
of the stock sold when 24 one-quarter pound blocks of fudge, 51 one-third pound bags of
gummies, and 84 one-twelfth pound bags of marshmallows are sold, what is x?
A. 24
B. 30
C. 35
D. 40 Correct Answer: D
Explanation: First let's find the value of 24/4+ 51/3+ 84/12. We have that 24/4= 6, 51/3= 17, and
84/12= 7. So 24/4+ 51/3+ 84/12is equal to 6 + 17 + 7, which is 30. So the question is now what
is the value of x if 30 is x% of 75? The fractional equivalent of x% is x100. So 30 = x/100(75).
Canceling a factor of 25 from the 75 and the 100 on the right side of this equation, we have that
30 = x/4(3). Then 30 = 3x/4, 120 = 3x, and x = 120/3= 40.
log8(64) - log64(8) =
A. −1/2
B. 1/2
C. 3/2
D. 5/2 Correct Answer: B
Explanation: Using the definition of logarithms, we know that log8(64) = 2, since 82 = 64.
Similarly, log64(8) = 1/2, since 64^1/2 = 8. Therefore, the expression given in the question,
log8(64) - log64(8) = 2 - 1/2 = 3/2.
A new law will impose a 18% sales tax on certain products sold in a state, where all other
products in the state are subject to a 6% sales tax when purchased. 18 percent of 18 is equal to 6
percent of
A. 6
B. 9
C. 54
D. 108 Correct Answer: C
Errorless Answers.
What is the range of the function below?
f(x) = 3x2- 5
A. (-∞, ∞)
B. (0, ∞)
C. (-5, ∞)
D. (5, ∞) Correct Answer: C
Explanation: The range of a function is the list of possible outputs of the function. It is
impossible for this function to generate any number less than -5, and there is no upper limit to
the output of this function. The range is (-5, ∞).
Which is equivalent to 3i2 + 2i4?
A. -1
B. 1
C. 5
D. 3 + 2i Correct Answer: A
Explanation: This question asks you to manipulate complex numbers. The key to solving this
problem is that i2 = -1. Substitute this into the expression:
3i2+2i4=3i2+2(i2)(i2)=3(−1)+2(−1)(−1)=−3+2=−1
If f(x)=x+25 , then what is f-1(x)?
A. x−2/5
B. 5x- 2
C. 5/x+2
D. 2−x/5 Correct Answer: B
Explanation: If the function is y=f(x)=x+2/5. To find the inverse function, switch x and y and
then solve for y:
x = y+2/5
5x = y+2
y = 5x-2
What is the sum of the two vectors (3 + 2i) and (-2 + i)?
A. 2 + 2i
B. -8
C. -6 + 2i
D. 1 + 3i Correct Answer: D
Explanation: To add vectors, group the real parts together and the imaginary parts together, and
then add:
, (3 + 2i) + (-2 + i) = (3 + -2) + (2i + i) = 1 + 3i
Which of the following is equivalent to (-2 + i)(3 + 2i)?
A. -8 -i
B. 1 + 3i
C. -6 + 2i
D. 5 + 3i Correct Answer: A
Explanation: To multiply two complex numbers, first distribute the parenthesis:
(-2 + i)(3 + 2i) = -6 + 3i- 4i + 2i2 = -6 - i + 2i2.
Then use the fact that i2 = -1:
-6 - i + 2 i2 =-6 - i + 2(-1) = -8 - i.
A candy store has 75 pounds of candy in stock at the beginning of the day. If x is the percentage
of the stock sold when 24 one-quarter pound blocks of fudge, 51 one-third pound bags of
gummies, and 84 one-twelfth pound bags of marshmallows are sold, what is x?
A. 24
B. 30
C. 35
D. 40 Correct Answer: D
Explanation: First let's find the value of 24/4+ 51/3+ 84/12. We have that 24/4= 6, 51/3= 17, and
84/12= 7. So 24/4+ 51/3+ 84/12is equal to 6 + 17 + 7, which is 30. So the question is now what
is the value of x if 30 is x% of 75? The fractional equivalent of x% is x100. So 30 = x/100(75).
Canceling a factor of 25 from the 75 and the 100 on the right side of this equation, we have that
30 = x/4(3). Then 30 = 3x/4, 120 = 3x, and x = 120/3= 40.
log8(64) - log64(8) =
A. −1/2
B. 1/2
C. 3/2
D. 5/2 Correct Answer: B
Explanation: Using the definition of logarithms, we know that log8(64) = 2, since 82 = 64.
Similarly, log64(8) = 1/2, since 64^1/2 = 8. Therefore, the expression given in the question,
log8(64) - log64(8) = 2 - 1/2 = 3/2.
A new law will impose a 18% sales tax on certain products sold in a state, where all other
products in the state are subject to a 6% sales tax when purchased. 18 percent of 18 is equal to 6
percent of
A. 6
B. 9
C. 54
D. 108 Correct Answer: C
