TestUstad

All Free Analytical and Logical Reasoning MCQs with Answers

Every Analytical and Logical Reasoning question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.

2,989 questions · page 92 of 150

1821. Roberto is an insurance agent who sells two types of policies: a $50,000 policy and a $100,000 policy. Last month, his goal was to sell at least 57 insurance policies. While he did not meet his goal, the total value of the policies he sold was over $3,000,000. Which of the following systems of inequalities describes x, the possible number of $50,000 policies, and y, the possible number of $100,000 policies, that Roberto sold last month?

  • A. x + y < 5750,000 x + 100,000 y < 3,000,000
  • B. x + y > 5750,000 x + 100,000 y > 3,000,000
  • C. x + y < 5750,000 x + 100,000 y > 3,000,000
  • D. x + y > 5750,000 x + 100,000 y < 3,000,000

Explanation: Choice C is correct. Since Roberto sells only two types of policies and he didn't meet his goal of selling at least 57 policies, the sum…

Read the full explanation →
Correct answer: x + y < 5750,000 x + 100,000 y > 3,000,000

1822. The table shows the results of a research study that investigated the therapeutic value of vitamin C in preventing colds. A random sample of 300 adults received either a vitamin C pill or a sugar pill each day during 2 weeks, and the adults reported whether they contracted a cold during that period. What proportion of adults who received a sugar pill reported contracting a cold?

  • A. 11/18
  • B. 11/50
  • C. 9/50
  • D. 11/100

Explanation: Choice B is correct. A total of 150 adults received the sugar pill. Of those, 33 reported contracting a cold.

Read the full explanation →
Correct answer: 11/50

1823. The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

  • A. 25,000 > (4,334 − 2,712)t
  • B. 25,000 < (4,334 − 2,712)t
  • C. 25,000 − 4,334 > 2,712t
  • D. 25,000 > (4,332/2,712)t

Explanation: Choice B is correct. The savings each year from installing the geothermal heating system will be the average annual energy cost for the…

Read the full explanation →
Correct answer: 25,000 < (4,334 − 2,712)t

1824. The 22 students in a health class conducted an experiment in which they each recorded their pulse rates, in beats per minute, before and after completing a light exercise routine. The dot plots below display the results.Let s1 and r1 be the standard deviation and range, respectively, of the data before exercise, and let s2 and r2 be the standard deviation and range, respectively, of the data after exercise. Which of the following is true?

  • A. s1 = s2 and r1 = r2
  • B. s1 < s2 and r1 < r2
  • C. s1 > s2 and r1 > r2
  • D. s1 ≠ s2 and r1 = r2

Explanation: Choice D is correct. The two data sets have the same range. The first data set has a range of 88 − 56 = 32, and the second data set has a…

Read the full explanation →
Correct answer: s1 ≠ s2 and r1 = r2

1825. In triangle RST above, point W (not shown) lies on RT. What is the value of cos(∠RSW ) − sin(∠WST )?

  • A. 0
  • B. 1
  • C. 2
  • D. 3

Explanation: The correct answer is 0. Note that no matter where point W is on _ RT, the sum of the measures of ∠RSW and ∠WST is equal to the measure of…

Read the full explanation →
Correct answer: 0

1826. 2x - y = 8x + 2y = 4For the system of equations above, what is the value of x + y?

  • A. -1
  • B. 4
  • C. 5
  • D. 20

Explanation: Choice B is correct. Multiplying both sides of the first equation in the system by 2 yields 4x − 2y = 16.

Read the full explanation →
Correct answer: 4

1827. The circle has center O, the length of arc ADC is 5π, and x = 100. What is the length of arc ABC?

  • A. 9π
  • B. 13π
  • C. 18π
  • D. 13/2π

Explanation: Choice B is correct. To find the length of arc ABC, first determine the measure of the central angle that subtends it.

Read the full explanation →
Correct answer: 13π

1828. (1/2x+1) + 5Which of the following is equivalent to the expression above for x > 0?

  • A. (2x + 5)/(2x + 1)
  • B. (2x + 6)/(2x + 1)
  • C. (10x + 5)/(2x + 1)
  • D. 10x + 6/2x + 1

Explanation: The correct answer is (10x + 6)/(2x + 1). To solve the expression (1/(2x+1)) + 5, you must first express the whole number 5 as a fraction…

Read the full explanation →
Correct answer: 10x + 6/2x + 1

1829. What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

  • A. 350
  • B. 360
  • C. 370
  • D. 380

Explanation: To find the volume of a right rectangular prism, you need to multiply its length, width, and height.

Read the full explanation →
Correct answer: 360

1830. Triangle PQR has a right angle Q. If sin R = 4/5, what is the value of tan P?

  • A. 1/4
  • B. 2/4
  • C. 3/4
  • D. 5/4

Explanation: The correct answer is 3/4, or 0.75. By definition of the sine ratio, since sin R = 4/5, PQ/PR = 4/5.

Read the full explanation →
Correct answer: 3/4

1831. During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?

  • A. Between 0 and 10 minutes
  • B. Between 30 and 40 minutes
  • C. Between 50 and 60 minutes
  • D. Between 90 and 100 minutes

Explanation: The correct answer is Choice A: Between 0 and 10 minutes. This interval shows the greatest decrease in temperature, meaning the average…

Read the full explanation →
Correct answer: Between 0 and 10 minutes

1832. In the figure, AD intersects BE at C. If x = 100, what is the value of y?

  • A. 100
  • B. 90
  • C. 80
  • D. 60

Explanation: Choice C is correct. The problem gives that x = 100, which is the measure of one angle in triangle ABC.

Read the full explanation →
Correct answer: 80

1833. A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

  • A. 2
  • B. 4
  • C. 5
  • D. 6

Explanation: Choice C is correct. Let a equal the number of 120-pound packages, and let b equal the number of 100-pound packages.

Read the full explanation →
Correct answer: 5

1834. If 2w + 4t = 14 and 4w + 5t = 25, what is the value of 2w +3t?

  • A. 6
  • B. 10
  • C. 13
  • D. 17

Explanation: The correct answer is 13. To solve the system, multiply the first equation, 2w + 4t = 14, by 2 to obtain 4w + 8t = 28.

Read the full explanation →
Correct answer: 13

1835. Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that the serving size of the cereal is 3/4 cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults.On Tuesday, Jennifer will mix Crunchy Grain cereal with Super Grain cereal for her breakfast. Super Grain cereal provides 240 calories per cup. If the total number of calories in one cup of Jennifer's mixture is 270, how much Super Grain cereal is in one cup of the mixture?

  • A. 1/8 cup
  • B. 1/4 cup
  • C. 1/3 cup
  • D. 1/2 cup

Explanation: Choice B is correct. It's given that a 3/4 cup serving of Crunch cereal provides 210 calories.

Read the full explanation →
Correct answer: 1/4 cup

1836. Near the end of a US cable news show, the host invited viewers to respond to a poll on the show's website that asked, "Do you support the new federal policy discussed during the show?" At the end of the show, the host reported that 28% responded "Yes," and 70% responded "No." Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?

  • A. The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.
  • B. Those who responded to the poll were not a random sample of the population of the United States.
  • C. A balanced 50% "Yes" and 50% "No" response was not achieved.
  • D. The show did not provide enough time for viewers to respond to the poll.

Explanation: The correct answer is that the respondents to the poll were not randomly selected from the population of the United States.

Read the full explanation →
Correct answer: Those who responded to the poll were not a random sample of the population of the United States.

1837. If sin x° = a, which of the following must be true for all values of x?

  • A. cos x° = a
  • B. sin (90o - xo) = a
  • C. cos (90o - xo ) = a
  • D. sin (x2)° = a2

Explanation: Choice C is correct. The sine of an angle is equal to the cosine of the angle's complement.

Read the full explanation →
Correct answer: cos (90o - xo ) = a

1838. Gisela would owe $15,500 in taxes each year if she were not eligible for any tax deductions. This year, Gisela is eligible for tax deductions that reduce the amount of taxes she owes by $2,325.00. If these tax deductions reduce the taxes Gisela owes this year by d%, what is the value of d?

  • A. 5
  • B. 10
  • C. 15
  • D. 20

Explanation: The correct answer is 15. To determine the percentage decrease, you use the formula: (Reduction Amount / Original Amount) * 100.

Read the full explanation →
Correct answer: 15

1839. x2 - 1/ x-1 = -2What are all values of x that satisfy the equation above?

  • A. -3
  • B. 0
  • C. 1
  • D. -3 and -1

Explanation: Choice A is correct. Factoring the numerator of the rational expression x2 − 1/ x − 1 yields (x + 1)(x − 1) / x − 1 .

Read the full explanation →
Correct answer: -3

1840. In the figure, triangle ABC is similar to triangle DEF. What is the value of cos(E)?

  • A. 12/5
  • B. 12/13
  • C. 5/12
  • D. 5/13

Explanation: Choice B is correct. Since figures are drawn to scale unless otherwise stated and triangle ABC is similar to triangle DEF, it follows that…

Read the full explanation →
Correct answer: 12/13
Start Free Analytical and Logical Reasoning Practice MCQs Test