All Analytical and Logical Reasoning MCQs

Question 1

In right triangle ABC, angle C is the right angle, and BC = 162. Point D on side AB is connected by a line segment with point E on side AC such that line segment DE is parallel to side BC and CE = 2AE. What is the length of line segment DE?

Accepted Answer

54

Answer

50

Answer

48

Answer

60

Question 2

The graph of function f is shown, where y = f(x).Which of the following describes function f?

Accepted Answer

Increasing linear

Answer

Decreasing linear

Answer

Increasing exponential

Answer

Decreasing exponential

Question 3

The graph of the function f is shown, where y = f(x) What is the y-intercept of the graph?

Accepted Answer

(0, −4)

Answer

(0, −1)

Answer

(0, 1)

Answer

(0, 4)

Question 4

The function f defined by f (t) = 14t + 9 gives the estimated length, in inches, of a vine plant t months after Tavon purchased it. Which of the following is the best interpretation of 9 in this context?

Accepted Answer

The estimated length of the vine plant was 9 inches when Tavon purchased it.

Answer

Tavon will keep the vine plant for 9 months.

Answer

The vine plant is expected to grow 9 inches each month.

Answer

The vine plant is expected to grow to a maximum length of 9 inches.

Question 5

A rectangle has an area of 155 square inches. The length of the rectangle is 4 inches less than 7 times the width of the rectangle. What is the width of the rectangle, in inches?

Accepted Answer

5

Answer

8

Answer

10

Answer

15

Question 6

4, 10, 18, 4, 4, 5, 6, 5 What is the median of the data set shown?

Accepted Answer

5

Answer

4

Answer

7

Answer

14

Question 7

A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is 24 square centimeters. What is the height, in centimeters, of the cylinder?

Accepted Answer

18

Answer

24

Answer

216

Answer

10,368

Question 8

The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. Which equation represents the linear relationship between c and p?

Accepted Answer

55c − p = −9

Answer

55c − p = 9

Answer

55p - c = -9

Answer

55p - c = 9

Question 9

If 48c = 3√47, what is the value of c?

Accepted Answer

7/24

Answer

7/20

Answer

7/10

Answer

7/15

Question 10

(x - 2) - 4 (y + 7) = 117(x - 2) + 4 (y + 7) = 442The solution to the given system of equations is (x, y). What is the value of 6(x - 2)?

Accepted Answer

1,677

Answer

1,660

Answer

1,665

Answer

1,680

Question 11

In triangle ABC, angle B is a right angle. The length of side AB is 10√37 and the length of side BC is 24√37. What is the length of the side AC?

Accepted Answer

26√37

Answer

14√37

Answer

34√37

Answer

√(34.37)

Question 12

x = y - 3x/2 + 2y = 6Which ordered pair (x, y) satisfies the system of equations shown above?

Accepted Answer

(0, 3)

Answer

(-3, 0)

Answer

(6, -3)

Answer

(36, -6)

Question 13

If f(x) = x2 - 6x + 3 / x - 1, what is f (-1)?

Accepted Answer

-5

Answer

-2

Answer

2

Answer

5

Question 14

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

Accepted Answer

640x + 880y ≤ 9,700x + y ≥ 10x ≥ 3y ≥ 1

Answer

640x + 880y ≥ 9,700x + y ≤ 10x ≥ 3y ≥ 1

Answer

640x + 880y ≥ 9,700x + y ≥ 10x ≤ 3y ≤ 1

Answer

640x + 880y ≤ 9,700x + y ≤ 10x ≤ 3y ≤ 1

Question 15

A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?

Accepted Answer

0 < x ≤ 10

Answer

0 < x ≤ 11 (2/3)

Answer

0 < x ≤ 17 (1/2)

Answer

0 < x ≤ 20

Question 16

The expression 1/3x2 - 2 can be rewritten as 1/3 (x - k)(x + k), where k is a positive constant. What is the value of k?

Accepted Answer

√6

Answer

2

Answer

6

Answer

√2

Question 17

The number of radians in a 720-degree angle can be written as aπ, where a is a constant. What is the value of a?

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 18

Which of the following ordered pairs (x, y) satisfies the inequality 5x −3y < 4?I. (1, 1)II. (2, 5)III. (3, 2)

Accepted Answer

I and II only

Answer

I only

Answer

II only

Answer

I and III only

Question 19

In the equation (ax + 3)2 = 36, a is a constant. If x = −3 is one solution to the equation, what is a possible value of a?

Accepted Answer

-1

Answer

-11

Answer

-5

Answer

0

Question 20

The scatterplot shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown.According to the scatterplot, which of the following statements is true about the relationship between a planetoid's average distance from the Sun and its density?

Accepted Answer

Planetoids that are more distant from the Sun tend to have lesser densities.

Answer

Planetoids that are more distant from the Sun tend to have greater densities.

Answer

The density of a planetoid that is twice as far from the Sun as another planetoid is exactly half the density of that other planetoid.

Answer

The distance from a planetoid to the Sun is unrelated to its density.

All Free Analytical and Logical Reasoning MCQs with Answers