MASS Math Test 1 — Questions and Answers
Question 1: Carlo left home with $6.50 in his purse. He spent $4.25 on foods and $2.00 on toys. Later, his friend returned the $2.50 he had borrowed the day before. How much money does Carlo currently have in his purse?
- $2.75 (Correct answer)
- $7.25
- $3.65
- $1.50
Correct answer: $2.75
To find out how much money Carlo has, you need to track his transactions. He started with $6.50, then spent $4.25 (leaving $2.25) and another $2.00 (leaving $0.25). Finally, his friend returned $2.50, so you add that to his current amount: $0.25 + $2.50 = $2.75.
Question 2: A combination lock has a three-digit code. Each digit can be any of the ten integers ranging from 0 to 9. How many possible combinations are there?
- 1000 (Correct answer)
- 500
- 200
- 100
Correct answer: 1000
For a three-digit code where each digit can be any of the ten integers from 0 to 9, you have 10 independent choices for each position. Therefore, the total number of possible combinations is found by multiplying the number of choices for each digit: 10 * 10 * 10 = 1000.
Question 3: There are sixteen empty chairs in Ms. Brittany's classroom. When every student is present, every chair is occupied. How many pupils make up her entire class if 2/5 of the students are absent?
- 40 (Correct answer)
- 38
- 26
- 52
Correct answer: 40
The problem states that 16 empty chairs mean 16 students are absent. It also specifies that 2/5 of the total students are absent. Therefore, 16 students represent 2/5 of the entire class. To find the total number of students, you can set up the equation (2/5) * Total Students = 16, and solve for Total Students: 16 * (5/2) = 40 students.
Question 4: Candidate A received 36,800 votes in a Boston County election. Candidate B came in second with 32,100 votes. Write-in candidates received 2,100 votes. Candidate A received what percentage of the vote?
- 51.80% (Correct answer)
- 43.21%
- 49.89%
- 23.45%
Correct answer: 51.80%
To find the percentage of votes Candidate A received, first calculate the total number of votes cast by summing the votes for Candidate A, Candidate B, and write-in candidates. This sum is 36,800 + 32,100 + 2,100 = 71,000 votes. Then, divide Candidate A's votes (36,800) by the total votes (71,000) and multiply by 100 to express it as a percentage, which yields approximately 51.80%.
Question 5: In the morning, Harry traveled 45 miles to work in an hour and ten minutes. However, traffic was much heavier on the way home, and the same drive took an hour and a half. What was his round-trip average speed in miles per hour?
- 33 3/4 mi/hr (Correct answer)
- 26 1/4 mi/hr
- 35 mi/hr
- 24 mi/hr
Correct answer: 33 3/4 mi/hr
To calculate the round-trip average speed, first determine the total distance traveled and the total time taken. The round-trip distance is 45 miles * 2 = 90 miles. The total time is 1 hour 10 minutes (7/6 hours) plus 1 hour 30 minutes (3/2 hours), which sums to 16/6 or 8/3 hours. Finally, divide the total distance (90 miles) by the total time (8/3 hours) to get the average speed, resulting in 33.75 miles per hour, or 33 3/4 mi/hr.
Question 6: Katy is half the age of her sister. In 20 years, she will be three-fourths her sister's age. How old is she?
- 10 (Correct answer)
- 5
- 12
- 14
Correct answer: 10
Let Katy's current age be K and her sister's current age be S. From the first statement, K = S/2. In 20 years, their ages will be K+20 and S+20, and the problem states K+20 = (3/4)(S+20). Substituting S = 2K into the second equation gives K+20 = (3/4)(2K+20), which simplifies to K+20 = (3/2)K + 15. Solving for K yields K = 10.
Question 7: A sailboat measures 19 meters. How many inches long is it?
- 38
- 748 (Correct answer)
- 320
- 190
Correct answer: 748
To convert meters to inches, you need to use standard conversion factors. First, convert 19 meters to centimeters by multiplying by 100 cm/meter, which gives 1900 cm. Then, convert centimeters to inches by dividing 1900 cm by the conversion factor of 2.54 cm/inch. This calculation results in approximately 748 inches.
MASS Math Test 1
Carlo left home with $6.50 in his purse.
He spent $4.25 on foods and $2.00 on toys.
Later, his friend returned the $2.50 he had borrowed the day before.
How much money does Carlo currently have in his purse?