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