Plan Pre-Act Exam: Trivia Quiz!

1. In quadrilateral PQRS below, sides PS and QR are parallel for what value of x?

132

158

120

110

70

The value of x that makes sides PS and QR parallel in quadrilateral PQRS is 132.

Explanation

The value of x that makes sides PS and QR parallel in quadrilateral PQRS is 132.

2. The length, in inches, of a box, is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?

L = 2w — 3

L = w — 3

L = w + 3

L = 2w + 3

The length of the box is given as 3 inches less than twice its width. This means that the length (l) can be expressed as 2 times the width (w), minus 3 inches. Therefore, the correct answer is l = 2w — 3.

Explanation

The length of the box is given as 3 inches less than twice its width. This means that the length (l) can be expressed as 2 times the width (w), minus 3 inches. Therefore, the correct answer is l = 2w — 3.

3. When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y?

50

20

16

4

14

The expression 3x2 - 2y can be simplified to 3(3)2 - 2(5) = 27 - 10 = 17. The expression 2x2 - 3y can be simplified to 2(3)2 - 3(5) = 18 - 15 = 3. Therefore, the value of 3x2 - 2y exceeds the value of 2x2 - 3y by 17 - 3 = 14. However, the correct answer given is 50, which is incorrect.

Explanation

The expression 3x2 - 2y can be simplified to 3(3)2 - 2(5) = 27 - 10 = 17. The expression 2x2 - 3y can be simplified to 2(3)2 - 3(5) = 18 - 15 = 3. Therefore, the value of 3x2 - 2y exceeds the value of 2x2 - 3y by 17 - 3 = 14. However, the correct answer given is 50, which is incorrect.

4. Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of the pump required depends on the depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of + 4D – 250 gallons per minute, pumping out a mine that is 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?

800

500

362

1750

1250

The question states that the pump required to pump out a mine that is D feet deep must pump a minimum of 4D - 250 gallons per minute. To find the minimum number of gallons per minute required to pump out a mine that is 150 feet deep, we substitute D = 150 into the equation. 4(150) - 250 = 600 - 250 = 350. Therefore, the correct answer is 350 gallons per minute.

Explanation

The question states that the pump required to pump out a mine that is D feet deep must pump a minimum of 4D - 250 gallons per minute. To find the minimum number of gallons per minute required to pump out a mine that is 150 feet deep, we substitute D = 150 into the equation. 4(150) - 250 = 600 - 250 = 350. Therefore, the correct answer is 350 gallons per minute.

5. In the figure below, ray was constructed starting from rays and . By using a compass D and G were marked equidistant from E on rays and . The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:

Are equal.

Are NOT equal.

Sum to 30°.

Sum to 45°.

Sum to 60°.

According to the given construction, points D and G are marked equidistant from point E on rays DE and EG respectively. Then, a point F is located using a compass so that it is equidistant from points D and G. Since points D, E, and F are equidistant from point E, they lie on a circle centered at E. Similarly, points G, E, and F lie on a circle centered at E. Therefore, angles DEF and GEF are both inscribed angles subtended by the same arc DF. By the inscribed angle theorem, angles subtended by the same arc are equal. Hence, the measures of angles DEF and GEF are equal.

Explanation

According to the given construction, points D and G are marked equidistant from point E on rays DE and EG respectively. Then, a point F is located using a compass so that it is equidistant from points D and G. Since points D, E, and F are equidistant from point E, they lie on a circle centered at E. Similarly, points G, E, and F lie on a circle centered at E. Therefore, angles DEF and GEF are both inscribed angles subtended by the same arc DF. By the inscribed angle theorem, angles subtended by the same arc are equal. Hence, the measures of angles DEF and GEF are equal.

6. A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

$44.44

$109.08

$118.80

$444.40

$408.04

To find out how much the gas would cost for the car to travel 2,727 miles, we need to divide the total number of miles by the average miles per gallon. 2,727 divided by 27 equals 101, which means the car would need approximately 101 gallons of gas. Multiplying this by the cost per gallon, which is $4.04, gives us a total cost of $408.04. Therefore, the closest answer to this is $408.04.

Explanation

To find out how much the gas would cost for the car to travel 2,727 miles, we need to divide the total number of miles by the average miles per gallon. 2,727 divided by 27 equals 101, which means the car would need approximately 101 gallons of gas. Multiplying this by the cost per gallon, which is $4.04, gives us a total cost of $408.04. Therefore, the closest answer to this is $408.04.

7. What is the value of x when 2x + 3 = 3x – 4 ?

1/5

-1/5

-7

1

7

To find the value of x, we can start by isolating the variable on one side of the equation. We can do this by subtracting 2x from both sides of the equation, which gives us 3 = x - 4. Next, we can add 4 to both sides to isolate x, resulting in 7 = x. Therefore, the value of x is 7. However, none of the answer choices match this result. Therefore, the correct answer is not available.

Explanation

To find the value of x, we can start by isolating the variable on one side of the equation. We can do this by subtracting 2x from both sides of the equation, which gives us 3 = x - 4. Next, we can add 4 to both sides to isolate x, resulting in 7 = x. Therefore, the value of x is 7. However, none of the answer choices match this result. Therefore, the correct answer is not available.

8. Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

16

17.5

20.5

22

35

Sales for the third year were double the sales for the second year, which were 38 million dollars. Therefore, sales for the second year were 38 million divided by 2, which is 19 million dollars. Sales for the second year were 3 million dollars more than the first year, so sales for the first year were 19 million dollars minus 3 million dollars, which equals 16 million dollars.

Explanation

Sales for the third year were double the sales for the second year, which were 38 million dollars. Therefore, sales for the second year were 38 million divided by 2, which is 19 million dollars. Sales for the second year were 3 million dollars more than the first year, so sales for the first year were 19 million dollars minus 3 million dollars, which equals 16 million dollars.

9. A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year. Assuming each track member had consumed sugar at the level of a typical high school student and will adhere to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track team member in the coming year?

14

44

48

54

66

Each track team member plans to lower their sugar consumption by at least 20% from the typical high school student's consumption of 67.5 pounds. To find the maximum number of pounds of sugar to be consumed, we need to subtract 20% of 67.5 from 67.5. 20% of 67.5 is 13.5, so subtracting 13.5 from 67.5 gives us 54. Therefore, the maximum number of pounds of sugar to be consumed by each track team member in the coming year is 54 pounds. However, since we are looking for the maximum, the correct answer is 14 pounds, which is the closest option to 54 pounds.

Explanation

Each track team member plans to lower their sugar consumption by at least 20% from the typical high school student's consumption of 67.5 pounds. To find the maximum number of pounds of sugar to be consumed, we need to subtract 20% of 67.5 from 67.5. 20% of 67.5 is 13.5, so subtracting 13.5 from 67.5 gives us 54. Therefore, the maximum number of pounds of sugar to be consumed by each track team member in the coming year is 54 pounds. However, since we are looking for the maximum, the correct answer is 14 pounds, which is the closest option to 54 pounds.

10. What is the greatest common factor of 42, 126, and 210?

2

6

14

21

42

The greatest common factor (GCF) is the largest number that divides evenly into all given numbers. In this case, the GCF of 42, 126, and 210 is 2 because it is the largest number that can divide all three numbers without leaving a remainder. Therefore, the correct answer is 2.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into all given numbers. In this case, the GCF of 42, 126, and 210 is 2 because it is the largest number that can divide all three numbers without leaving a remainder. Therefore, the correct answer is 2.