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Gordon purchased a television when his local electronics store had a sale. The television was offered at 30% off its original price of $472. What was the sale price Gordon paid?
- A. $141.60
- B. $225.70
- C. $305.30
- D. $330.40
Correct Answer: D
Rationale: To find the sale price after a 30% discount, you need to subtract 30% of the original price from the original price. 30% of $472 is $141.60. Subtracting this discount from the original price gives $472 - $141.60 = $330.40, which is the sale price Gordon paid. Choice A, $141.60, is incorrect as it represents only the discount amount, not the final sale price. Choices B and C are also incorrect as they do not account for the correct calculations of the discount and final sale price.
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Simplify the following expression: 5 x 3 · 9 x 4
- A. 5/12
- B. 8/13
- C. 20/27
- D. 47/36
Correct Answer: A
Rationale: To simplify the expression 5 x 3 · 9 x 4, first perform the multiplications and divisions from left to right: 5 x 3 = 15 and 9 x 4 = 36. So, the expression becomes 15 · 36. When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. Hence, 15 · 36 = 15/36. To simplify the fraction further, find the greatest common divisor, which is 3. Divide both the numerator and denominator by 3 to get the final result: 15/36 = 5/12. Therefore, the correct answer is A. Choices B, C, and D are incorrect because they do not represent the correct simplification of the given expression.
A can has a radius of 1.5 inches and a height of 3 inches. Which of the following best represents the volume of the can?
- A. 17.2 in³
- B. 19.4 in³
- C. 21.2 in³
- D. 23.4 in³
Correct Answer: C
Rationale: The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. Substituting the given values (r = 1.5 inches, h = 3 inches) into the formula yields V ≈ 21.2 in³. Therefore, the correct answer is C. Choice A, 17.2 in³, is incorrect as it does not correspond to the correct calculation. Choice B, 19.4 in³, is also incorrect and does not match the calculated volume. Choice D, 23.4 in³, is not the correct volume obtained when using the provided dimensions in the formula for the volume of a cylinder.
Given the histograms shown below, which of the following statements is true?
- A. Group A is negatively skewed and has a mean less than Group B.
- B. Group A is positively skewed and has a mean greater than Group B.
- C. Group B is negatively skewed and has a mean greater than Group A.
- D. Group B is positively skewed and has a mean less than Group A.
Correct Answer: C
Rationale: The correct answer is C. Group B is negatively skewed, indicating more high scores, leading to a higher mean for Group B when compared to Group A. Choice A is incorrect because Group A is not negatively skewed and doesn't have a mean less than Group B. Choice B is incorrect as Group A is not positively skewed and its mean is not greater than Group B. Choice D is also incorrect because Group B having a mean less than Group A contradicts the fact that Group B has a higher mean due to being negatively skewed.
A patient requires a 30% increase in the dosage of their medication. Their current dosage is 270 mg. What will their dosage be after the increase?
- A. 81 mg
- B. 270 mg
- C. 300 mg
- D. 351 mg
Correct Answer: D
Rationale: To calculate the 30% increase, find 30% of 270 mg: 0.30 x 270 mg = 81 mg. Add this increase to the original dosage: 270 mg + 81 mg = 351 mg. Therefore, the patient's dosage after the 30% increase will be 351 mg. Choice A (81 mg) is incorrect as it only represents the calculated increase, not the total dosage post-increase. Choice B (270 mg) is the original dosage and does not account for the 30% increase. Choice C (300 mg) is the original dosage plus 30 mg, not the correct calculation with a 30% increase.
In a study where 60% of respondents use smartphones to check their email, and 5,000 respondents were included, how many respondents use smartphones for email?
- A. 3,000 respondents
- B. 2,500 respondents
- C. 5,000 respondents
- D. 1,000 respondents
Correct Answer: A
Rationale: In the study, 60% of 5,000 respondents using smartphones for email would equal 3,000 respondents, not the total number of respondents. Therefore, the correct answer is 3,000 respondents. Choice B, 2,500 respondents, is incorrect because it doesn't consider the percentage of smartphone users. Choice C, 5,000 respondents, is incorrect as it represents the total number of respondents, not the specific number using smartphones for email. Choice D, 1,000 respondents, is incorrect as it is not the correct calculation based on the given information.