All Analytical and Logical Reasoning MCQs

Question 1

Some values of x and their corresponding values of y are shown in the table, where a is a constant. If there is a linear relationship between x and y, which of the following equations represents the relationship?

Accepted Answer

x + 2y = a

Answer

x + 2y = 5a

Answer

2x - y = -5a

Answer

2x - y = 7a

Question 2

700, 1200, 1600, 2000, xIf the mean of the five numbers above is 1600, what is the value of x?

Accepted Answer

2500

Answer

2300

Answer

2400

Answer

2600

Question 3

Tilly earns p dollars for every w hours of work. Which expression represents the amount of money, in dollars, Tilly earns for 39w hours of work?

Accepted Answer

39p

Answer

p/39

Answer

p + 39

Answer

p - 39

Question 4

For the right triangle shown, a = 4 and b = 5. Which expression represents the value of c ?

Accepted Answer

√42 + 52

Answer

4 + 5

Answer

√(4)(5)

Answer

√4 + 5

Question 5

The equation E(t) = 5(1.8)t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

Accepted Answer

The estimated number of employees when the restaurant opened

Answer

The increase in the estimated number of employees each year

Answer

The number of years the restaurant has been open

Answer

The percent increase in the estimated number of employees each year

Question 6

Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

Accepted Answer

Increasing exponential

Answer

Decreasing exponential

Answer

Decreasing linear

Answer

Increasing linear

Question 7

The population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k ?

Accepted Answer

1.07

Answer

0.07

Answer

0.7

Answer

1.7

Question 8

An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?

Accepted Answer

16

Answer

0.07

Answer

15

Answer

27

Question 9

If 4x − 4 = 112, what is the positive value of x − 1 ?

Accepted Answer

28

Answer

18

Answer

38

Answer

40

Question 10

What is the y-intercept of the graph shown?

Accepted Answer

(0, 8)

Answer

(−8, 0)

Answer

(−6, 0)

Answer

(0, 6)

Question 11

The function f is defined by f(x) = x3 + 15. What is the value of f (2) ?

Accepted Answer

23

Answer

20

Answer

21

Answer

24

Question 12

Each side of a square has a length of 45. What is the perimeter of this square?

Accepted Answer

180

Answer

120

Answer

170

Answer

200

Question 13

Sean rents a tent at a cost of $11 per day plus a onetime insurance fee of $10. Which equation represents the total cost c, in dollars, to rent the tent with insurance for d days?

Accepted Answer

c = 11d +10

Answer

c = 11(d + 10)

Answer

c = 10(d + 11)

Answer

c = 10d +11

Question 14

John paid a total of $165 for a microscope by making a down payment of $37 plus p monthly payments of $16 each. Which of the following equations represents this situation?

Accepted Answer

16p + 37 = 165

Answer

16p − 37 = 165

Answer

37p − 16 = 165

Answer

37p + 16 = 165

Question 15

A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg,did the rocket burn each second after launch

Accepted Answer

4,995

Answer

17,243

Answer

39,481

Answer

104,895

Question 16

The graph represents the total charge, in dollars, by an electrician for x hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

Accepted Answer

The electrician's hourly rate

Answer

The total amount that the electrician charges

Answer

The electrician's onetime fee

Answer

The maximum amount that the electrician charges

Question 17

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

Accepted Answer

24

Answer

6

Answer

10

Answer

14

Question 18

A small business owner budgets $2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and$11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

Accepted Answer

182

Answer

4.9

Answer

7

Answer

9

Question 19

Triangle FGH is similar to triangle JKL, where angle F corresponds to angle J and angles G and K are right angles. If sin (F) = 308 / 317, what is the value of sin ( J ) ?

Accepted Answer

308/317

Answer

75/317

Answer

317/308

Answer

317/75

Question 20

The circle has center O, circumference 144π,and diameters PR and QS. The length of arc PS is twice the length of arc PQ. What is the length of arc QR ?

Accepted Answer

48π

Answer

24π

Answer

72π

Answer

96π

All Free Analytical and Logical Reasoning MCQs with Answers