1. There are 20 boxes of cereal on a store shelf, and exactly 5 of these boxes have a prize. What is the ratio of the number of boxes with a prize to the number of boxes without a prize?
A. 1:3 Correct
B. 1:4
C. 1:5
D. 2:3
Explanation
The number of boxes with a prize is 5. The number of boxes without a prize is 20 - 5 = 15. The ratio of boxes with a prize to boxes without a prize is 5:15, which simplifies to 1:3 by dividing both terms by 5. Choice B (1:4) is the ratio of prize boxes to total boxes. Choice C (1:5) is incorrect. Choice D (2:3) does not result from the given numbers.
2. Maria walks x yards in 15 minutes. If she continues to walk at the same average rate, how many more yards will she walk in the next 7 minutes?
A. 15x/7
B. (x/15)+7
C. (x+7)/15
D. 7x/15 Correct
Explanation
Maria's walking rate is x/15​ yards per minute. The distance walked in 7 minutes at this rate is 7* x/15​ = 7x/15 yards. Choice A inverts the rate and time. Choice B adds 7 to the rate, which is dimensionally incorrect. Choice C adds 7 minutes to the distance and divides by time, which is not the correct application of the rate formula.
3. Which of the following is equal to |7 - 5|?
A. |7| + |-5|
B. |5| - |7|
C. |5 - 7| Correct
D. |-7 + (-5)|
Explanation
The absolute value of ∣7−5∣=∣2∣=2. ∣5−7∣=∣−2∣=2, so choice C is correct. Choice A is ∣7∣+∣−5∣=7+5=12. Choice B is ∣5∣−∣7∣=5−7=−2. Choice D is ∣−7+(−5)∣=∣−12∣=12.
4. If the average (arithmetic mean) of g and 100 is 75, what is the value of g + 100?
A. 50
B. 125
C. 150 Correct
D. 175
Explanation
The average of g and 100 is g + 100/2= 75. Multiplying both sides by 2 gives g + 100 = 150. Choice A is half of 100. Choice B is 125, which is the average if g were 50. Choice D is 175, which is not supported by the equation.
5. Which of the following is equivalent to the inequality above?
A. x > -4
B. x > -2
C. x < 2
D. x < 4 Correct
Explanation
Solving the inequality: 8 - 2x > 2x - 8. Add 2x to both sides: 8 > 4x - 8. Add 8 to both sides: 16 > 4x. Divide both sides by 4: 4 > x, which is equivalent to x < 4. Choice A results from incorrect sign handling. Choice B and C are not derived from the correct algebraic manipulation.