ACCUPLACER QUANTITATIVE REASONING
ALGEBRA AND STATISTICS | 2026
COMPREHENSIVE EXAM QUESTIONS AND
COMPLETE SOLUTIONS
Which of the following expressions is 5 times as much as the sum of r and s?
A. 5 x r + s
B. 5 + r + s
C. r + s x 5
D. (r + s) x 5 - Answer~D. (r + s) x 5
The order of operations was used properly to write the expression. The sum of r and s
in parenthesis is found first, then multiplication is used to find the number that is 5
times the sum of r and s.
What is the solution to the equation
1/2X + 3/2(x + 1) - 1/4 = 5 ?
A. 5/2
B. 13/8
C. 15/8
D. 17/8 - Answer~C. 15/8
The equation can be rewritten as 1/2X + 3/2X + 3/2 - 1/4 = 5, which simplifies to 2X = 5
+ 1/4 - 3/2 = 5/14.
Therefore, X = 15/ = 15/8.
What is the number of grams in 500 kilograms? (1 kilogram = 1,000 grams)
A. 0.5
, B. 5,000
C. 50,000
D. 500,000 - Answer~D. 500,000
To convert from kilograms to grams, multiply 500 kg x 1,000g/1kg, which results in
500,000 grams.
(graph) Robert sells four different flavors of jam at an annual farmers market. The
graph above shows the number of jars of each type of jam he sold at the market during
the first two hours. Which flavor of jam had the greatest increase in number of jars sold
from Year 1 to Year 2?
A. Blueberry
B. Grape
C. Peach
D. Strawberry - Answer~A. Blueberry
The graph shows that he sold 10 jars if blueberry jam the first year and 18 the second
year, for an increase of 8 jars. This is the largest increase of any of the flavors.
In the xy- plane, a line crosses the y-axis at the point (0,3) and passes through the point
(4,5). Which of the following is an equation of the line?
A. y = 1/2X + 3
B. y = 2X + 3
C. y = 1/2X - 4
D. y = 2x - 4 - Answer~A. y = 1/2X + 3
An equation in the form y = ax + b has a slope of a and a y-intercept of b. The line
described has a y-intercept of 3 because it crosses the y-axis at y = 3 and has a slope of
1./2 because the value of y increases by 1 for every x increase of 2. Therefore, an
equation of the line is y = 1/2X + 3.
ALGEBRA AND STATISTICS | 2026
COMPREHENSIVE EXAM QUESTIONS AND
COMPLETE SOLUTIONS
Which of the following expressions is 5 times as much as the sum of r and s?
A. 5 x r + s
B. 5 + r + s
C. r + s x 5
D. (r + s) x 5 - Answer~D. (r + s) x 5
The order of operations was used properly to write the expression. The sum of r and s
in parenthesis is found first, then multiplication is used to find the number that is 5
times the sum of r and s.
What is the solution to the equation
1/2X + 3/2(x + 1) - 1/4 = 5 ?
A. 5/2
B. 13/8
C. 15/8
D. 17/8 - Answer~C. 15/8
The equation can be rewritten as 1/2X + 3/2X + 3/2 - 1/4 = 5, which simplifies to 2X = 5
+ 1/4 - 3/2 = 5/14.
Therefore, X = 15/ = 15/8.
What is the number of grams in 500 kilograms? (1 kilogram = 1,000 grams)
A. 0.5
, B. 5,000
C. 50,000
D. 500,000 - Answer~D. 500,000
To convert from kilograms to grams, multiply 500 kg x 1,000g/1kg, which results in
500,000 grams.
(graph) Robert sells four different flavors of jam at an annual farmers market. The
graph above shows the number of jars of each type of jam he sold at the market during
the first two hours. Which flavor of jam had the greatest increase in number of jars sold
from Year 1 to Year 2?
A. Blueberry
B. Grape
C. Peach
D. Strawberry - Answer~A. Blueberry
The graph shows that he sold 10 jars if blueberry jam the first year and 18 the second
year, for an increase of 8 jars. This is the largest increase of any of the flavors.
In the xy- plane, a line crosses the y-axis at the point (0,3) and passes through the point
(4,5). Which of the following is an equation of the line?
A. y = 1/2X + 3
B. y = 2X + 3
C. y = 1/2X - 4
D. y = 2x - 4 - Answer~A. y = 1/2X + 3
An equation in the form y = ax + b has a slope of a and a y-intercept of b. The line
described has a y-intercept of 3 because it crosses the y-axis at y = 3 and has a slope of
1./2 because the value of y increases by 1 for every x increase of 2. Therefore, an
equation of the line is y = 1/2X + 3.
