Compass Math Pool 1 — Questions and Answers
Question 1: If a gas tank can hold 30 gallons, how many gallons does it contain when it is three-fifths full?
- 15
- 12
- 24
- 18 (Correct answer)
Correct answer: 18
To find three-fifths of 30 gallons, you multiply the total capacity by the fraction. (3/5) * 30 = 90/5 = 18. Therefore, the tank contains 18 gallons when it is three-fifths full.
Question 2: If x = y, what does 4(x-y) + 7 =?
- 4x - 4y + 7
- 7 (Correct answer)
- 4xy + 7
- 11x - 11y
Correct answer: 7
Given that x = y, the term (x-y) in the expression becomes (x-x) or (y-y), which simplifies to 0. Substituting this into the expression, we get 4(0) + 7. This simplifies further to 0 + 7, which equals 7.
Question 3: In a bag of candy, there are 4 Tootsie Rolls, 3 Lollipops, 5 Hershey Kisses and 6 Starbursts. If you select one piece of candy at random, what is the probability that it will be a lollipop?
- 1/18
- 1/6 (Correct answer)
- 3/10
- 1/4
Correct answer: 1/6
To calculate the probability of selecting a lollipop, divide the number of lollipops by the total number of candies. There are 3 lollipops and a total of 4+3+5+6 = 18 candies. So, the probability is 3/18, which simplifies to 1/6.
Question 4: If 0.05z = 1, then z =
- 2
- 20 (Correct answer)
- 200
- 0.05
Correct answer: 20
To solve for z, you need to isolate it by dividing both sides of the equation by 0.05. So, z = 1 / 0.05. Dividing 1 by 0.05 (or 1 by 5/100) gives you 1 * (100/5), which equals 20.
Question 5: How long will it take to reach a town 250 miles a way if you drive 50 miles per hour?
- 4 hours
- 5 hours (Correct answer)
- 10 hours
- 6 hours
Correct answer: 5 hours
To find the time it takes to travel a certain distance, you use the formula Time = Distance / Rate. Given a distance of 250 miles and a rate of 50 miles per hour, the time taken is 250 / 50, which equals 5 hours.
Question 6: A toll is $2 for a car and the driver and 75 cent for each additional passenger. If the toll comes to $4.25, how many total people are in the car?
- 6
- 5
- 3
- 4 (Correct answer)
Correct answer: 4
First, subtract the base toll for the car and driver ($2.00) from the total toll ($4.25) to find the cost for additional passengers, which is $2.25. Then, divide this amount by the cost per additional passenger ($0.75) to find that there are 3 additional passengers. Finally, add the driver to the additional passengers (1 + 3) to get a total of 4 people in the car.
Question 7: (x+3)(x+5) = A. x2+16x +8 B. x2+16x+15 C. x2+8x+15 D. x2+8x+8
- A
- B
- C (Correct answer)
- D
Correct answer: C
Use the FOIL method (First, Outside, Inside, Last) to solve. X2 +3x +5x + 3x5
Question 8: (x+4)(x+4) = A. x2+16x +8 B. x2+16x+16 C. x2+8x+16 D. x2+8x+8
- A
- B
- C (Correct answer)
- D
Correct answer: C
Use the FOIL method (First, Outside, Inside, Last) to solve. X2 +4x +4x + 4x4
Question 9: Tina bought a scarf for $16.65. She gave the clerk $20. How much change should she get back?
- $4.35
- $3.45
- $3.35 (Correct answer)
- $3.25
Correct answer: $3.35
To find out how much change Tina should receive, subtract the cost of the scarf from the amount she paid. Tina paid $20.00 and the scarf cost $16.65. Performing the subtraction, $20.00 - $16.65 equals $3.35. Therefore, Tina should get $3.35 back in change.
Question 10: A product originally costs $125. If the product goes on sale for 20% off, and then goes on sale for an additional 30% off, what is the price of the product?
- $62.50
- $70 (Correct answer)
- $65
- $90
Correct answer: $70
You need to apply the discounts successively not just add the discounts. So $125 x 80% = $100 (price after original 20% discount). $100 x 70% = $70 the price after the 2nd 30% discount.
Compass Math Pool 1
If a gas tank can hold 30 gallons, how many gallons does it contain when it is three-fifths full?