Choose the best answer. If necessary, use the paper you were given.
Which of the following is equal to 3 * 9?
- A. 6 * 6
- B. 9 * 3
- C. 3 * 3 * 6
- D. 3 * 3 * 3 * 3
Correct Answer & Rationale
Correct Answer: B
Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.
Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.
Other Related Questions
Last year Joan's salary was $18,000. If she receives a $900 raise for this year, what percent of last year's salary is her raise?
- A. 2%
- B. 5%
- C. 20%
- D. 50%
Correct Answer & Rationale
Correct Answer: B
To find the percentage of last year's salary that Joan's raise represents, divide the raise amount by last year's salary and then multiply by 100. Here, $900 (raise) divided by $18,000 (last year's salary) equals 0.05. Multiplying by 100 gives 5%, which is the correct answer. Option A (2%) miscalculates the raise as a smaller fraction of the salary. Option C (20%) incorrectly interprets the raise as a larger proportion, perhaps confusing it with a different calculation. Option D (50%) vastly overestimates the raise, suggesting it is half of last year's salary, which is not accurate.
To find the percentage of last year's salary that Joan's raise represents, divide the raise amount by last year's salary and then multiply by 100. Here, $900 (raise) divided by $18,000 (last year's salary) equals 0.05. Multiplying by 100 gives 5%, which is the correct answer. Option A (2%) miscalculates the raise as a smaller fraction of the salary. Option C (20%) incorrectly interprets the raise as a larger proportion, perhaps confusing it with a different calculation. Option D (50%) vastly overestimates the raise, suggesting it is half of last year's salary, which is not accurate.
Of the following, which is closest to (2(12/15) - 1/10) / (16/6)?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
Maria worked 2 weeks, earning $435.50 the first week and $278.38 the second week. If she paid one-half of her two-week earnings for tuition, how much did she pay for tuition?
- A. $713.88
- B. $356.94
- C. $217.75
- D. $139.19
Correct Answer & Rationale
Correct Answer: B
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
If 40 is 20 percent of a number, then the number is what percent of 40?
- A. 500%
- B. 200%
- C. 80%
- D. 20%
Correct Answer & Rationale
Correct Answer: A
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.