QRB 501 Final Exam Answers QRB 501 Final Exam 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 – x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression using x as the variable: A number decreased by 25 and multiplied by 4 A. x – 25 · 4 B. -25x · 4 C. 4x - 25 D. 4(x – 25) 3. Write the following as an algebraic expression using x as the variable: The sum of a number and -8 A. -8 + x B. -8 - x C. x (-8) D. -8x 4) Write the following as an algebraic expression using x as the variable: Twelve less than six times a number A. 12 – 6x B. –6x C. –12(6x) D. 6x – 12 5) Solve: -3 – (-2 + 4) - 5 A. 15 B. 10 C. -6 D. -10 6) Solve: (–5)2 · (9 – 17)2 ÷ (–10)2 A. 16 B. 64 C. -6.4 D. -.039 7) Solve: 3(32) – 8(9 – 2) ÷ 2 A. -14.5 B. 55 C. 66.5 D. -1 8) Solve: (–5)2 · (9 – 17)2 ÷ (–10)2 A. 16 B. 64 C. -6.4

1. QRB 501 Final Exam
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QRB 501 Final Exam Answers
QRB 501 Final Exam
1) Write the following as an algebraic expression using x as the variable:

2. Triple a number subtracted from the number
A. 3(x - x)
B. x 3 – x
C. 3x - x
D. x - 3x
2) Write the following as an algebraic expression using x as the variable: A
number decreased by 25 and multiplied by 4
A. x – 25 · 4
B. -25x · 4
C. 4x - 25
D. 4(x – 25)
3. Write the following as an algebraic expression using x as the variable: The
sum of a number and -8
A. -8 + x
B. -8 - x
C. x (-8)
D. -8x
4) Write the following as an algebraic expression using x as the variable:
Twelve less than six times a number

3. A. 12 – 6x
B. –6x
C. –12(6x)
D. 6x – 12
5) Solve: -3 – (-2 + 4) - 5
A. 15
B. 10
C. -6
D. -10
6) Solve: (–5)2 · (9 – 17)2 ÷ (–10)2
A. 16
B. 64
C. -6.4
D. -.039
7) Solve: 3(32) – 8(9 – 2) ÷ 2
A. -14.5
B. 55
C. 66.5
D. -1
8) Solve: (–5)2 · (9 – 17)2 ÷ (–10)2

4. A. 16
B. 64
C. -6.4
D. -.039
9) Solve: 3(-19 + 4) ÷ -5
A. 9
B. -13.8
C. 0.11
D. 13.8
10) Solve: –9 + 18 ÷ –3(–6)
A. 27
B. 90
C. -0.5
D. 0.5
11) Identify the variable, constant, and coefficient of the expression: 10k –
15
A. variable: k; constant: –15; coefficient: 10
B. variable: k; constant: 15; coefficient: 10
C. variable: 10; constant: k; coefficient: –15

5. D. variable: 15; constant: 10; coefficient: k
12) Identify the variable, constant, and coefficient of the expression: x – y
A. variable: x and y; constant: 0; coefficient: 0
B. variable: x and y; constant: 0; coefficient: 1
C. variable: y; constant: x; coefficient: 0
D. variable: x; constant: –y; coefficient: 1
13) Identify the variable, constant, and coefficient of the expression: 3p
A. variable: p; constant: 0; coefficient: 3
B. variable: 3; constant: 0; coefficient:
C. variable: 3; constant: p; coefficient: 3
D. variable: p; constant: 3; coefficient: 0
14) Solve the system of equations:
4x + 3y = 1
3x + 2y = 2
A. { (1,–1) }
B. { (4, – 5) }
C. { (–1,2) }
D. { (–2,3) }
15) Solve the system of equations:
3x – 5y = 7

6. 2x + 3y = 30
A. { (6,1) }
B. { (9,4) }
C. { (–1,–2) }
D. { (3,8) }
16) Solve the system of equations:
3x + 2y = 18
y = 3x
A. { (4,3) }
B. { (2,6) }
C. { (1,3) }
D. { (3,9) }
17) Solve the system of equations:
3x = 7 – y
2y = 14 – 6x
A. { (x,y) ¦ 3x + y = 7 }
B. { (x,y) ¦ –3x + y = 7 }
C. { (x,y) ¦ 2x + y = 3 }
D. { (x,y) ¦ x + y = 2 }

7. 18) Solve the system of equations:
3x + y = –7
x – y = –5
A. { (– 3,2) }
B. { (–4,1) }
C. { (–2,–1) }
D. { (1,–8) }
19) The Manager of Engineering reported that the industrial production index
was 135. What does this production mean?
A. An increase of 35 units
B. An increase of 35 percent
C. Not enough information given
D. A decrease of 35 percent
20) Which of the following is true of a base period for an index number?
A. It cannot be less than 100
B. The numerator spears
C. It must have occurred after the year 1980
D. It appears in the denominator
21) Which of the following is true of an index?
A. It shows a percent change from one period to another

8. B. It must be larger than 100
C. It cannot assume negative values
D. It can employ qualitative data
22) A man earned $80,000 when the Consumer Price Index was 200. What
were his earnings in terms of $2,000 if the base period was 2000?
A. $40,000
B. $160,000
C. $60,000
D. $80,000
23) What happens as we increase the number of classes in a histogram?
A. Central tendency becomes more obvious
B. Class interval width increases
C. There would be more classes
D. Class intervals become rounder
24) On which axis is time plotted on a simple line chart?
A. On the Y-axis
B. On the X-axis
C. Time is not plotted
D. Either axis

9. 25) The monthly incomes for a group of engineers are: $2,200, $2,400,
$2,600, $3,100, $3,400, and $3,700. What are these ungrouped numbers
called?
A. Class limits
B. Histograms
C. Raw data
D. Class frequencies
26) What is the term for a number of observations in a class in a frequency
distribution?
A. Class interval
B. Class midpoint
C. Class array
D. Class frequency
27) Why are unequal class intervals sometimes used in a frequency
distribution?
A. To avoid a large number of empty classes
B. To create variety in presenting the data
C. To avoid the need for midpoints
D. To make the class frequencies smaller
28) What is the slope of the line: 14y – 2x = 28

10. A. -2
B. 1/7
C. 7
D. 2
29) What is the slope of the line: 5y – x = 10
A. 2
B. 1/5
C. 1/2
D. -1
30) What is the slope of the line: 36x – 9y = 15
A. 4
B. 36
C. 3
D. -5/3
31) What is the slope of the line: 2y + 8x = 26
A. 8
B. -4
C. 2
D. 1/4

11. 32) What is the slope of the line: 3x – y = 6
A. 3
B. 2
C. -1
D. ½
33) Which statement is true regarding the estimated slope of a linear
regression line?
A. It is chosen so as to minimize the sum of squared errors.
B. It shows the change in x for a unit change in y.
C. It could curve up or down as it moves to the right.
D. It is always positive.
34) Which statement is true of a regression line that is superimposed on the
scatter plot?
A. It guarantees the largest possible sample variance.
B. It is computed using the Ordinary Least Squares method.
C. It guarantees that the slope and intercept are minimized.
D. It is computed using the maximum and minimum values.
35) Which of the following is observed in a scatter plot when there is an
inverse relationship between x and y?
A. Points are mostly in the lower left and upper right quadrants.

12. B. Points create a horizontal line.
C. Points slope down as it moves to the right.
D. Points curve up as it moves to the right.
36) What happens to the future value of money when the inflation rate
exceeds the interest rate?
A. Decreases
B. Increases
C. Stays the same
D. Not enough information
37) Since money has the ability to earn interest, its value increases with
time. What affects the future value of an investment more, the interest rate
or the time the investment is held?
A. The interest rate has a larger impact on the future value of the investment.
B. The length of time has more of an impact on the future value of the investment.
C. It depends on the interest rate and the time the investment is held.
D. Both interest and length of time have the same impact on the future value of the
investment
38) The number of hours spent studying appears to be highly correlated with
the grade students earn in a class. Which variable would be the dependent

13. variable in a linear regression analysis?
A. Hours spent studying
B. Either variable could be the dependent variable
C. The class average
D. The grade earned
39) When interest is compounded, the total time period is subdivided into
several interest periods, for example 1 year, 3 months, 1 month. How does
compound interest affect the future value of an investment?
A. Stays the same
B. Increases
C. Decreases
D. Not enough information
40) When the interest rate is positive, what happens to the value of money
as we move from the future to the present?
A. Stays the same
B. Decreases
C. Increases
D. Not enough information
41) What is the principal balance if the principal plus interest at the end of
1.5 years is $3,360 at an annual interest rate of 8%?

14. A. $2,000
B. $2,800
C. $3,000
D. $2,200
42) How is the class midpoint calculated?
A. Find the difference between consecutive lower limits.
B. Count the number of observations in the class.
C. Divide the class interval in half and add the result to the lower limit.
D. frequency by the number of observations
43) How is a frequency distribution converted to a relative frequency
distribution?
A. Find the difference between consecutive lower class limits.
B. Divide the lower limit of the first class by the class interval
C. Multiply the class frequency by 100
D. Divide the class frequency by the total number of observations
44) What does the horizontal axis of a line chart represent?
A. Dollars
B. Variable quantity
C. Percent

15. D. Time
45) Which measures of central tendency are not affected by extremely low or
extremely high values?
A. Mean and median
B. Mode and median
C. Only the mean
D. Mean and mode
46) For which measure of central tendency will the sum of the deviations
always be zero?
A. Mode
B. Median
C. Mode and Median
D. Mean
47) Which measure of dispersion represents variation from the mean?
A. Range
B. Spread
C. Outliers
D. Standard deviation
48) Which of the following is true regarding the normal distribution?
A. Mean, median and mode are all equal

16. B. It is not always symmetrical
C. The total area under the curve is greater than 1
D. It can have more than one peak
49) Which of the following is a characteristic of a normal distribution?
A. Positively skewed
B. Can be either positively or negatively skewed
C. Has a total z-score of 1000
D. Symmetrical
50) What is the proportion of the total area under the normal curve within
plus or minus 2 standard deviations?
A. 68%
B. 95%
C. 100%
D. 99.7%
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