DAT Quantitative
Reasoning Practice
Questions
2026
Master Exam Prep Bundle
(Verified Questions & Answers)
A+ Grade Guaranteed
,If tan θ = 5/12 and sin θ > 0, then cos θ = ? b. 12/13
a. -5/12 tanθ = opp/adj = 5/12
b. 12/13 c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13
c. 13/12 cosθ = adj/hyp = 12/13
d. -12/13
e. 0
If 60% of x equal to 30% of 20, then what is the value of (x e. 225
+ 5)^2?
0.6x = (0.3) x 20 → x = 10
a. 25.25 (x + 5)^2 → (10 + 5)^2 = (15)^2 = 225
b. 26
c. 26.01
d. 2025
e. 225
In the xy-plane, the point (4,3) and (3,2) are on line A. e. y = x
Which of the following equations of lines is parallel to line
A? Slope of line A is:
m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1
a. y = 3x Parallel lines have the same slope and only choice (e.) has slope of 1.
b. y = 10
c. y = x2
d. y = 2x
e. y = x
When point A (10,3) is reflected over the y-axis to get the c. (-10,3)
point B, what are the coordinates of point B?
When points reflected over y-axis, the value of y in the coordinates doesn't change
a. (10,3) and the sign of the x changes. Therefore, the coordinate point B is (-10, 3).
b. (-10,-3)
c. (-10,3)
d. (10,-3)
e. (0,3)
If f(x) = 2x^3 + 5x^2 + 2x and g(x) = -2, what is the value of e. 0
f(g(x))?
g(x) = -2, then f(g(x)) = f(-2)
a. 36 f(-2) = 2(-2)^3 + 5(-2)^2 + 2(-2)
b. 32 = -16 + 20 - 4 = 0
c. 24
d. 4
e. 0
In the equation x = [8y + (r/r + 1)] / [(6/z)], when z is b. x is divided by 3
divided by 3, what is the effect on x?
x = [8y + (r/r + 1)] / [(6/(z/3))]
a. x is divided by 2 x = [8y + (r/r + 1)] / [(3 x 6/(z)]
b. x is divided by 3 x/3 = [8y + (r/r + 1)] / [(3 x 6/(z)] x (1/3)
c. x does not change
d. x is multiplied by 3
e. x is multiplied by 2
A boat sails 40 miles south and then 30 miles east. How b. 50 miles
far is the boat from its start point?
Use Pythagorean Theorem: a^2 + b^2 = c^2
a. 45 miles 40^2 + 30^2 = c^2
b. 50 miles → 1600 + 900 = c^2
c. 60 miles → 2500 = c^2 → c = 50
d. 70 miles
e. 80 miles
2026
, x is y% of what number? a. 100x/y
a. 100x/y Let the number be A. Then:
b. 100y/x x = y% * A
c. x/100y Solve for A.
d. y/100x x = y/100 * A
e. xy/100 Multiply both sides by 100/y:
x 100/y = y/100 100/y * A
A = 100x/y
If cotangent of an angle β is 1, then tangent of angle β is c. 1
a. -1 Tangent = 1/cotangent = 1
b. 0
c. 1
d. 2
e. 3
What is the value of y in the following system of e. 5
equations?
3x - 4y = -20
-x + 2y = 10
a. -1
b. -2
c. 1
d. 4
e. 5
How long does a 420-mile trip take moving at 50 miles per c. 8 hours and 24 minutes
hour (mph)?
a. 4 hours
b. 6 hours and 24 minutes
c. 8 hours and 24 minutes
d. 8 hours and 30 minutes
e. 10 hours and 30 minutes
When 40% of 60 is added to 12% of 600, the resulting c. 96
number is:
a. 24
b. 72
c. 96
d. 140
e. 180
A ladder leans against a wall forming a 60o angle between d. 60 feet
the ground and the ladder. If the bottom of the ladder is 30
feet away from the wall, how long is the ladder?
a. 30 feet
b. 40 feet
c. 50 feet
d. 60 feet
e. 120 feet
If 40% of a class are girls, and 25% of girls play tennis, a. 10
what percentage of the class play tennis?
a. 10
b. 15
c. 20
d. 40
e. 80
2026
Reasoning Practice
Questions
2026
Master Exam Prep Bundle
(Verified Questions & Answers)
A+ Grade Guaranteed
,If tan θ = 5/12 and sin θ > 0, then cos θ = ? b. 12/13
a. -5/12 tanθ = opp/adj = 5/12
b. 12/13 c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13
c. 13/12 cosθ = adj/hyp = 12/13
d. -12/13
e. 0
If 60% of x equal to 30% of 20, then what is the value of (x e. 225
+ 5)^2?
0.6x = (0.3) x 20 → x = 10
a. 25.25 (x + 5)^2 → (10 + 5)^2 = (15)^2 = 225
b. 26
c. 26.01
d. 2025
e. 225
In the xy-plane, the point (4,3) and (3,2) are on line A. e. y = x
Which of the following equations of lines is parallel to line
A? Slope of line A is:
m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1
a. y = 3x Parallel lines have the same slope and only choice (e.) has slope of 1.
b. y = 10
c. y = x2
d. y = 2x
e. y = x
When point A (10,3) is reflected over the y-axis to get the c. (-10,3)
point B, what are the coordinates of point B?
When points reflected over y-axis, the value of y in the coordinates doesn't change
a. (10,3) and the sign of the x changes. Therefore, the coordinate point B is (-10, 3).
b. (-10,-3)
c. (-10,3)
d. (10,-3)
e. (0,3)
If f(x) = 2x^3 + 5x^2 + 2x and g(x) = -2, what is the value of e. 0
f(g(x))?
g(x) = -2, then f(g(x)) = f(-2)
a. 36 f(-2) = 2(-2)^3 + 5(-2)^2 + 2(-2)
b. 32 = -16 + 20 - 4 = 0
c. 24
d. 4
e. 0
In the equation x = [8y + (r/r + 1)] / [(6/z)], when z is b. x is divided by 3
divided by 3, what is the effect on x?
x = [8y + (r/r + 1)] / [(6/(z/3))]
a. x is divided by 2 x = [8y + (r/r + 1)] / [(3 x 6/(z)]
b. x is divided by 3 x/3 = [8y + (r/r + 1)] / [(3 x 6/(z)] x (1/3)
c. x does not change
d. x is multiplied by 3
e. x is multiplied by 2
A boat sails 40 miles south and then 30 miles east. How b. 50 miles
far is the boat from its start point?
Use Pythagorean Theorem: a^2 + b^2 = c^2
a. 45 miles 40^2 + 30^2 = c^2
b. 50 miles → 1600 + 900 = c^2
c. 60 miles → 2500 = c^2 → c = 50
d. 70 miles
e. 80 miles
2026
, x is y% of what number? a. 100x/y
a. 100x/y Let the number be A. Then:
b. 100y/x x = y% * A
c. x/100y Solve for A.
d. y/100x x = y/100 * A
e. xy/100 Multiply both sides by 100/y:
x 100/y = y/100 100/y * A
A = 100x/y
If cotangent of an angle β is 1, then tangent of angle β is c. 1
a. -1 Tangent = 1/cotangent = 1
b. 0
c. 1
d. 2
e. 3
What is the value of y in the following system of e. 5
equations?
3x - 4y = -20
-x + 2y = 10
a. -1
b. -2
c. 1
d. 4
e. 5
How long does a 420-mile trip take moving at 50 miles per c. 8 hours and 24 minutes
hour (mph)?
a. 4 hours
b. 6 hours and 24 minutes
c. 8 hours and 24 minutes
d. 8 hours and 30 minutes
e. 10 hours and 30 minutes
When 40% of 60 is added to 12% of 600, the resulting c. 96
number is:
a. 24
b. 72
c. 96
d. 140
e. 180
A ladder leans against a wall forming a 60o angle between d. 60 feet
the ground and the ladder. If the bottom of the ladder is 30
feet away from the wall, how long is the ladder?
a. 30 feet
b. 40 feet
c. 50 feet
d. 60 feet
e. 120 feet
If 40% of a class are girls, and 25% of girls play tennis, a. 10
what percentage of the class play tennis?
a. 10
b. 15
c. 20
d. 40
e. 80
2026
