DAT Quantitative Reasoning Practice d d d d
Questions With Verified Answers d d d
If tan θ = 5/12 and sin θ > 0, then cos θ = ?
d d d d d d d d d d d d d d
a. -5/12d
b. 12/13d
c. 13/12
d
d. -12/13
d
e. 0 - d d d
d d d d d d d d d d d d d d d b. 12/13 d
tanθ = opp/adj = 5/12 d d d d
c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13
d d d d d d d d d d d d
cosθ = adj/hyp = 12/13 d d d d
If 60% of x equal to 30% of 20, then what is the value of (x + 5)^2?
d d d d d d d d d d d d d d d d d
a. 25.25d
b. 26 d
c. 26.01
d
d. 2025 d
e. 225 -d d d
d d d d d d d d d d d d d d d e. 225
d
0.6x = (0.3) x 20 → x = 10
d d d d d d d d
(x + 5)^2 → (10 + 5)^2 = (15)^2 = 225
d d d d d d d d d d
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,In the xy-plane, the point (4,3) and (3,2) are on line A. Which of the following equations of lines is
d d d d d d d d d d d d d d d d d d d d
parallel to line A? d d d
a. y = 3x
d d d
b. y = 10
d d d
c. y = x2
d d d
d. y = 2x
d d d
e. y = x -
d d d d d
d d d d d d d d d d d d d d d e. y = x
d d d
Slope of line A is: d d d d d
m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1
d d d d d d d d d d d d d d
Parallel lines have the same slope and only choice (e.) has slope of 1.
d d d d d d d d d d d d d
When point A (10,3) is reflected over the y-axis to get the point B, what are the coordinates of
d d d d d d d d d d d d d d d d d d d
point B? d
a. (10,3)
d
b. (-10,-3)
d
c. (-10,3)
d
d. (10,-3)
d
e. (0,3) -
d d d
d d d d d d d d d d d d d d d c. (-10,3)
d
When points reflected over y-axis, the value of y in the coordinates doesn't change and the sign of
d d d d d d d d d d d d d d d d d d
the x changes. Therefore, the coordinate point B is (-10, 3).
d d d d d d d d d d
If f(x) = 2x^3 + 5x^2 + 2x and g(x) = -2, what is the value of f(g(x))?
d d d d d d d d d d d d d d d d d
a. 36 d
b. 32 d
c. 24d
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,d. 4 d
e. 0 - d d d
d d d d d d d d d d d d d d d e. 0 d
g(x) = -2, then f(g(x)) = f(-2)
d d d d d d
f(-2) = 2(-2)^3 + 5(-2)^2 + 2(-2)
d d d d d d
= -16 + 20 - 4 = 0
d d d d d d d
In the equation x = [8y + (r/r + 1)] / [(6/z)], when z is divided by 3, what is the effect on x?
d d d d d d d d d d d d d d d d d d d d d d d
a. x is divided by 2
d d d d d
b. x is divided by 3
d d d d d
c. x does not change
d d d d
d. x is multiplied by 3
d d d d d
e. x is multiplied by 2 -
d d d d d d d
d d d d d d d d d d d d d d d b. x is divided by 3
d d d d d
x = [8y + (r/r + 1)] / [(6/(z/3))]
d d d d d d d d
x = [8y + (r/r + 1)] / [(3 x 6/(z)]
d d d d d d d d d d
x/3 = [8y + (r/r + 1)] / [(3 x 6/(z)] x (1/3)
d d d d d d d d d d d d
A boat sails 40 miles south and then 30 miles east. How far is the boat from its start point?
d d d d d d d d d d d d d d d d d d d
a. 45 miles
d d
b. 50 miles
d d
c. 60 miles
d d
d. 70 miles
d d
e. 80 miles -
d d d d
d d d d d d d d d d d d d d d b. 50 miles
d d
Use Pythagorean Theorem: a^2 + b^2 = c^2
d d d d d d d
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, 40^2 + 30^2 = c^2 d d d d d
→ 1600 + 900 = c^2
d d d d d
→ 2500 = c^2 → c = 50
d d d d d d d
x is y% of what number?
d d d d d
a. 100x/y
d
b. 100y/x
d
c. x/100y
d
d. y/100x
d
e. xy/100 -
d d d
d d d d d d d d d d d d d d d a. 100x/y d
Let the number be A. Then:
d d d d d
x = y% * A
d d d d
Solve for A. d d
x = y/100 * A
d d d d
Multiply both sides by 100/y: d d d d
x * 100/y = y/100 * 100/y * A
d d d d d d d d
A = 100x/y
d d
If cotangent of an angle β is 1, then tangent of angle β is
d d d d d d d d d d d d d
a. -1 d
b. 0 d
c. 1 d
d. 2 d
e. 3 - d d d
d d d d d d d d d d d d d d d c. 1 d
Tangent = 1/cotangent = 1 d d d d
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Questions With Verified Answers d d d
If tan θ = 5/12 and sin θ > 0, then cos θ = ?
d d d d d d d d d d d d d d
a. -5/12d
b. 12/13d
c. 13/12
d
d. -12/13
d
e. 0 - d d d
d d d d d d d d d d d d d d d b. 12/13 d
tanθ = opp/adj = 5/12 d d d d
c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13
d d d d d d d d d d d d
cosθ = adj/hyp = 12/13 d d d d
If 60% of x equal to 30% of 20, then what is the value of (x + 5)^2?
d d d d d d d d d d d d d d d d d
a. 25.25d
b. 26 d
c. 26.01
d
d. 2025 d
e. 225 -d d d
d d d d d d d d d d d d d d d e. 225
d
0.6x = (0.3) x 20 → x = 10
d d d d d d d d
(x + 5)^2 → (10 + 5)^2 = (15)^2 = 225
d d d d d d d d d d
1|Page
,In the xy-plane, the point (4,3) and (3,2) are on line A. Which of the following equations of lines is
d d d d d d d d d d d d d d d d d d d d
parallel to line A? d d d
a. y = 3x
d d d
b. y = 10
d d d
c. y = x2
d d d
d. y = 2x
d d d
e. y = x -
d d d d d
d d d d d d d d d d d d d d d e. y = x
d d d
Slope of line A is: d d d d d
m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1
d d d d d d d d d d d d d d
Parallel lines have the same slope and only choice (e.) has slope of 1.
d d d d d d d d d d d d d
When point A (10,3) is reflected over the y-axis to get the point B, what are the coordinates of
d d d d d d d d d d d d d d d d d d d
point B? d
a. (10,3)
d
b. (-10,-3)
d
c. (-10,3)
d
d. (10,-3)
d
e. (0,3) -
d d d
d d d d d d d d d d d d d d d c. (-10,3)
d
When points reflected over y-axis, the value of y in the coordinates doesn't change and the sign of
d d d d d d d d d d d d d d d d d d
the x changes. Therefore, the coordinate point B is (-10, 3).
d d d d d d d d d d
If f(x) = 2x^3 + 5x^2 + 2x and g(x) = -2, what is the value of f(g(x))?
d d d d d d d d d d d d d d d d d
a. 36 d
b. 32 d
c. 24d
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,d. 4 d
e. 0 - d d d
d d d d d d d d d d d d d d d e. 0 d
g(x) = -2, then f(g(x)) = f(-2)
d d d d d d
f(-2) = 2(-2)^3 + 5(-2)^2 + 2(-2)
d d d d d d
= -16 + 20 - 4 = 0
d d d d d d d
In the equation x = [8y + (r/r + 1)] / [(6/z)], when z is divided by 3, what is the effect on x?
d d d d d d d d d d d d d d d d d d d d d d d
a. x is divided by 2
d d d d d
b. x is divided by 3
d d d d d
c. x does not change
d d d d
d. x is multiplied by 3
d d d d d
e. x is multiplied by 2 -
d d d d d d d
d d d d d d d d d d d d d d d b. x is divided by 3
d d d d d
x = [8y + (r/r + 1)] / [(6/(z/3))]
d d d d d d d d
x = [8y + (r/r + 1)] / [(3 x 6/(z)]
d d d d d d d d d d
x/3 = [8y + (r/r + 1)] / [(3 x 6/(z)] x (1/3)
d d d d d d d d d d d d
A boat sails 40 miles south and then 30 miles east. How far is the boat from its start point?
d d d d d d d d d d d d d d d d d d d
a. 45 miles
d d
b. 50 miles
d d
c. 60 miles
d d
d. 70 miles
d d
e. 80 miles -
d d d d
d d d d d d d d d d d d d d d b. 50 miles
d d
Use Pythagorean Theorem: a^2 + b^2 = c^2
d d d d d d d
3|Page
, 40^2 + 30^2 = c^2 d d d d d
→ 1600 + 900 = c^2
d d d d d
→ 2500 = c^2 → c = 50
d d d d d d d
x is y% of what number?
d d d d d
a. 100x/y
d
b. 100y/x
d
c. x/100y
d
d. y/100x
d
e. xy/100 -
d d d
d d d d d d d d d d d d d d d a. 100x/y d
Let the number be A. Then:
d d d d d
x = y% * A
d d d d
Solve for A. d d
x = y/100 * A
d d d d
Multiply both sides by 100/y: d d d d
x * 100/y = y/100 * 100/y * A
d d d d d d d d
A = 100x/y
d d
If cotangent of an angle β is 1, then tangent of angle β is
d d d d d d d d d d d d d
a. -1 d
b. 0 d
c. 1 d
d. 2 d
e. 3 - d d d
d d d d d d d d d d d d d d d c. 1 d
Tangent = 1/cotangent = 1 d d d d
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