How many digits are in the Hindu-Arabic numeral system?
- A. Two
- B. Ten
- C. Twelve
- D. Twenty
Correct Answer: B
Rationale: The Hindu-Arabic numeral system consists of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten digits are used as the fundamental symbols to represent numbers in this numerical system. Choice A, 'Two,' is incorrect as there are more than two digits in the system. Choice C, 'Twelve,' is incorrect as it exceeds the total number of digits in the system. Choice D, 'Twenty,' is incorrect as it overestimates the number of digits present in the Hindu-Arabic numeral system.
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If Gwen's favorite summer drink is 2 parts fruit juice to 3 parts seltzer and she starts with a gallon of fruit juice, how many quarts of seltzer will she need?
- A. 3 quarts
- B. 4.5 quarts
- C. 5 quarts
- D. 6 quarts
Correct Answer: D
Rationale: To maintain the ratio of 2 parts fruit juice to 3 parts seltzer, for every 2 parts of fruit juice, Gwen will need 3 parts of seltzer. Since a gallon of fruit juice is equivalent to 4 quarts, she will need 3 quarts of seltzer for every 2 quarts of fruit juice. For 4 quarts of fruit juice, she will require 6 quarts of seltzer. Therefore, Gwen will need 6 quarts of seltzer to make the summer drink for her friends. Choice A (3 quarts) is incorrect because it does not account for the correct ratio. Choice B (4.5 quarts) is incorrect because it is not a whole number and does not align with the ratio provided. Choice C (5 quarts) is incorrect as it does not match the proportional ratio of fruit juice to seltzer required.
Rectangle: A picture frame measures 15cm by 20cm. What is its perimeter?
- A. 30cm
- B. 55cm
- C. 65cm
- D. 75cm
Correct Answer: C
Rationale: To find the perimeter of a rectangle, you add the lengths of all sides. The formula for the perimeter of a rectangle is 2 * (length + width). In this case, the length is 15cm and the width is 20cm. Therefore, the perimeter = 2 * (15cm + 20cm) = 65cm. Choice A (30cm), Choice B (55cm), and Choice D (75cm) are incorrect as they do not correctly calculate the perimeter of the given rectangle.
Chun Mei earns a 5% commission on each appliance she sells. If she sells a washer for $749 and a dryer for $689, what will her commission be?
- A. $37.45
- B. $71.90
- C. $149.80
- D. $287.60
Correct Answer: B
Rationale: To calculate Chun Mei's commission, we first find the total sales amount by adding the prices of the washer and dryer: $749 + $689 = $1438. Next, we calculate her 5% commission on this total sales amount: 0.05 * $1438 = $71.90. Therefore, Chun Mei's commission for selling both appliances will be $71.90. Choice B, $71.90, is the correct answer. Choices A, C, and D are incorrect as they do not reflect the accurate calculation of Chun Mei's commission based on the given scenario.
Subtract and simplify: 8¼ − 1½.
- A. 4¼
- B. 6¾
- C. 6â…ž
- D. 7¼
Correct Answer: A
Rationale: To subtract mixed numbers, convert them to improper fractions. 8¼ = 33/4 and 1½ = 3/2. Subtracting, we get 33/4 - 3/2 = 33/4 - 6/4 = 27/4 = 6¾, which simplifies to 4¼. Therefore, the correct answer is 4¼. Choice B is incorrect as it represents the intermediate step of 6¾ before simplification. Choice C is incorrect as it is the result of the subtraction but not simplified. Choice D is incorrect as it is the original mixed number 7¼, not the simplified result.
Multiply: 32 5 and express the result in decimal form.
- A. 0.0016
- B. 0.016
- C. 0.16
- D. 1.6
Correct Answer: D
Rationale: To find the product of 32 and 5, you simply multiply the two numbers: 32 5 = 160. Therefore, when expressed in decimal form, the answer is 1.6. Choices A, B, and C are incorrect as they do not represent the correct multiplication result in decimal form. Choice A is way too small, choice B is also too small, and choice C is close but still not the correct result.