Free College Math Placement Basic Math Question and Answers — Questions and Answers
Question 1: All students receive a 10% reduction from the original instrument price from a music supply outlet. Back-to-school sales typically subtract an additional 15% from the already-discounted price. Mary, a high school student in the area, spends $306 on a flute. How much did it cost at first?
- 400 (Correct answer)
- 325
- 450
- 430
Correct answer: 400
Let the original price of the flute be P. A 10% reduction means the price becomes P * (1 - 0.10) = 0.90P. An additional 15% reduction is applied to this discounted price, so it becomes (0.90P) * (1 - 0.15) = 0.90P * 0.85. We know Mary paid $306, so 0.90P * 0.85 = $306. Multiplying the decimals gives 0.765P = $306. To find the original price P, divide $306 by 0.765: P = $306 / 0.765 = $400.
Question 2: Which of the following numbers is NOT equal to 34(58+9)?
- 34 * 58 + 34 * 9
- 34 * 67
- 1,972 + 306
- 58(34+9) (Correct answer)
Correct answer: 58(34+9)
The original expression is 34(58+9). This represents 34 multiplied by the sum of 58 and 9. Options A, B, and C are all equivalent to this expression through direct calculation or the distributive property. Option D, 58(34+9), incorrectly switches the multiplier; it would expand to 58*34 + 58*9, which is not the same as 34*58 + 34*9. Therefore, 58(34+9) is not equal to the original expression.
Question 3: In a recipe for cookies, which of the following units should be used to measure the sugar?
- quarts
- liters
- kilograms
- cups (Correct answer)
Correct answer: cups
In typical cooking and baking recipes, especially for ingredients like sugar, measurements are commonly given by volume. Among the given options, 'cups' is the standard unit of volume used for measuring sugar in a recipe. Quarts and liters are larger volume units, and kilograms measure mass, which is less common for home baking recipes.
Question 4: John sold a yacht that he had himself designed for a 15% profit after paying $15,000 for it. How much was the boat sold for?
- $16,540.44
- $17,250.00 (Correct answer)
- $15,980.55
- $16,230.34
Correct answer: $17,250.00
To find the selling price, first calculate the profit amount. A 15% profit on the original cost of $15,000 is calculated as 0.15 * $15,000 = $2,250. The selling price is the original cost plus the profit. Therefore, John sold the boat for $15,000 + $2,250 = $17,250.00.
Question 5: Suppose a rectangular house's length is 22 feet and its perimeter is 25 1/3 yards. How wide is it?
- 35 feet
- 40 feet
- 16 feet (Correct answer)
- 37 feet
Correct answer: 16 feet
First, convert the perimeter from yards to feet. Since 1 yard equals 3 feet, 25 1/3 yards is equivalent to 25.333... * 3 = 76 feet. The formula for the perimeter of a rectangle is P = 2(length + width). We know P = 76 feet and length = 22 feet. Substitute these values: 76 = 2(22 + width). Divide both sides by 2: 38 = 22 + width. Finally, subtract 22 from both sides to find the width: width = 38 - 22 = 16 feet.
Question 6: Lisa's base pay is $90 per week, and she also gets a 12% commission on all purchases. This week, Lisa brought in $3,000 in sales. How much money did she make overall?
- $450 (Correct answer)
- $480
- $510
- $525
Correct answer: $450
To find Lisa's total earnings, first calculate her commission. Her commission is 12% of her $3,000 in sales, which is 0.12 * $3,000 = $360. Her total money made overall is the sum of her base pay and her commission. So, $90 (base pay) + $360 (commission) = $450.
Question 7: How much money did Jane save in May 2001 if she only used 20% of the allotted amount for food rather than the full 25%?
- $144.30
- $131.10 (Correct answer)
- $152.22
- $153.33
Correct answer: $131.10
The savings represent the difference between the original allotted percentage for food (25%) and the percentage actually used (20%), applied to the total budget. This means Jane saved 5% (25% - 20%) of her total budget. If the savings amount to $131.10, we can find the total budget (B) by setting up the equation 0.05B = $131.10. Solving for B, B = $131.10 / 0.05 = $2622. The $131.10 saved is 5% of this implied total budget.
Free College Math Placement Basic Math Question and Answers
All students receive a 10% reduction from the original instrument price from a music supply outlet.
Back-to-school sales typically subtract an additional 15% from the already-discounted price.
Mary, a high school student in the area, spends $306 on a flute.
How much did it cost at first?