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After taxes, a worker earned $15,036 in 7 months. What is the amount the worker earned in 2 months?
- A. $2,148
- B. $4,296
- C. $6,444
- D. $8,592
Correct Answer: B
Rationale: To find the amount earned in 2 months, set up a proportion using two ratios relating amount earned to months: (15,036/7) = (x /2). Cross-multiply and solve for x: 7x = 30,072, x = 4,296. Therefore, the worker earned $4,296 in 2 months. Choice A, $2,148, is incorrect as it is half of the correct answer. Choices C and D, $6,444 and $8,592, are incorrect as they do not correspond to the calculated proportion.
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4 − 1/(22) + 24 · (8 + 12). Simplify the expression. Which of the following is correct?
- A. 1.39
- B. 2.74
- C. 4.95
- D. 15.28
Correct Answer: C
Rationale: First, complete the operations in parentheses: 4 − (1/22) + 24 · 20. Next, simplify the exponents: 4 − (1/22) + 24 · 20 = 4 − (1/4) + 24 · 20. Then, complete multiplication and division operations: 4 − (1/4) + 24 · 20 = 4 − 0.25 + 1.2. Finally, complete addition and subtraction operations: 4 − 0.25 + 1.2 = 4.95. Choice A, 1.39, is incorrect as it does not match the correct calculation. Choice B, 2.74, is incorrect as it is not the result of the given expression. Choice D, 15.28, is incorrect as it is not the correct simplification of the initial expression.
A woman's dinner bill comes to $48.30. If she adds a 20% tip, which of the following will be her total bill?
- A. $9.66
- B. $38.64
- C. $48.30
- D. $57.96
Correct Answer: D
Rationale: To calculate the total bill after adding a 20% tip, you need to find 120% of the original bill. This is because adding a 20% tip means paying 120% of the bill. So, $48.30 120/100 = $57.96. Therefore, the correct answer is $57.96. Choice A ($9.66) is incorrect as it represents only the 20% tip amount. Choice B ($38.64) is incorrect as it is the original bill amount without the tip. Choice C ($48.30) is incorrect as it is the original bill amount and does not include the additional 20% tip.
x · 7 = x − 36. Solve the equation. Which of the following is correct?
- A. x = 6
- B. x = 42
- C. x = 4
- D. x = 252
Correct Answer: B
Rationale: To solve the equation x · 7 = x − 36, start by multiplying both sides by 7 to get 7(x · 7) = 7(x − 36), which simplifies to x = 7x − 252. Next, subtract 7x from both sides to get -6x = -252. Finally, divide both sides by -6 to solve for x, which results in x = 42. Therefore, the correct answer is x = 42. Choice A (x = 6), Choice C (x = 4), and Choice D (x = 252) are incorrect as they do not align with the correct solution derived from the equation.
What is the result of (4.71 10^3) - (2.98 10^2)? Which of the following is the correct simplified expression?
- A. 1.73 10
- B. 4.412 10^2
- C. 1.73 10^3
- D. 4.412 10^3
Correct Answer: D
Rationale: The correct answer is D: 4.412 10^3. To simplify the expression, rewrite 4.71 10^3 as 47.1 10^2. Subtract the values in front of 10^2: 47.1 - 2.98 = 44.12. Rewriting this gives 44.12 10^2 = 4.412 10^3. Choice A is incorrect as it does not account for the correct subtraction result. Choice B is incorrect as it does not correctly simplify the expression. Choice C is incorrect as it provides an incorrect power of 10 in the simplified expression.
What is the perimeter of a rectangle with a length of 12 cm and a width of 5 cm?
- A. 17 cm
- B. 24 cm
- C. 34 cm
- D. 40 cm
Correct Answer: C
Rationale: The correct formula for the perimeter of a rectangle is P = 2(l + w), where l represents the length and w represents the width. Substituting the given values into the formula: P = 2(12 cm + 5 cm) = 2(17 cm) = 34 cm. Therefore, the perimeter of the rectangle is 34 cm. Choice A (17 cm) is incorrect as it seems to have added only the length and width without multiplying by 2. Choice B (24 cm) is incorrect as it does not consider the multiplication by 2. Choice D (40 cm) is incorrect as it seems to have added the length and width without multiplying by 2.