A bowl contains 18 pieces of candy: 8 red, 6 orange, and 4 green. Brandon will select 1 piece of candy at random. What is the probability that Brandon will select a green piece?
- A. 2/7
- B. 2/9
- C. 2/11
- D. 1/9
- E. 1/8
Correct Answer & Rationale
Correct Answer: B
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
Other Related Questions
Which of the following intervals most likely represents the average gas mileage, in miles per gallon, of 50% of the cars?
- A. 20 to 32
- B. 24 to 32
- C. 29 to 32
- D. 30 to 44
- E. 32 to 44
Correct Answer & Rationale
Correct Answer: B
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
The recommended dosage of a medicine is 4 milligrams per kilogram of body weight. What is the recommended dosage, in milligrams, for a person who weighs 84 kilograms?
- A. 21
- B. 88
- C. 324
- D. 336
- E. 2100
Correct Answer & Rationale
Correct Answer: D
To determine the recommended dosage for a person weighing 84 kilograms, multiply their weight by the dosage per kilogram: 4 mg/kg × 84 kg = 336 mg. Option A (21 mg) is incorrect as it significantly underestimates the dosage based on the weight. Option B (88 mg) also miscalculates the dosage, failing to apply the correct multiplication. Option C (324 mg) is close but still incorrect, as it does not reflect the accurate calculation. Option E (2100 mg) is far too high, indicating a misunderstanding of the dosage per kilogram. Thus, 336 mg is the correct dosage for the individual.
To determine the recommended dosage for a person weighing 84 kilograms, multiply their weight by the dosage per kilogram: 4 mg/kg × 84 kg = 336 mg. Option A (21 mg) is incorrect as it significantly underestimates the dosage based on the weight. Option B (88 mg) also miscalculates the dosage, failing to apply the correct multiplication. Option C (324 mg) is close but still incorrect, as it does not reflect the accurate calculation. Option E (2100 mg) is far too high, indicating a misunderstanding of the dosage per kilogram. Thus, 336 mg is the correct dosage for the individual.
One online movie-streaming service costs $8 per month and charges $1.50 per movie. A second service costs $2 per month and charges $2 per movie. For what number of movies per month is the monthly cost of both services the same?
- A. 3
- B. 6
- C. 5
- D. 12
- E. 20
Correct Answer & Rationale
Correct Answer: D
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
Emma measured the height of her laptop screen. She reported the height as 8 inches, accurate to the nearest inch. The actual height of the screen must be:
- A. at least 7.5 inches and less than 8.5 inches
- B. at least 7.9 inches and less than 8.1 inches
- C. at least 7.99 inches and less than 8.01 inches
- D. at least 8 inches
- E. exactly 8 inches
Correct Answer & Rationale
Correct Answer: A
When measuring to the nearest inch, values can range from halfway to the next whole number. For Emma's reported height of 8 inches, this means the actual height must be at least 7.5 inches (inclusive) and less than 8.5 inches (exclusive). Option B is too narrow, only allowing for heights between 7.9 and 8.1 inches, which does not encompass all possible values. Option C is even more restrictive, only allowing for heights between 7.99 and 8.01 inches, excluding valid measurements. Option D is incorrect as it suggests the height must be 8 inches or more, which is too limiting. Option E incorrectly states the height must be exactly 8 inches, disregarding the range of possible values.
When measuring to the nearest inch, values can range from halfway to the next whole number. For Emma's reported height of 8 inches, this means the actual height must be at least 7.5 inches (inclusive) and less than 8.5 inches (exclusive). Option B is too narrow, only allowing for heights between 7.9 and 8.1 inches, which does not encompass all possible values. Option C is even more restrictive, only allowing for heights between 7.99 and 8.01 inches, excluding valid measurements. Option D is incorrect as it suggests the height must be 8 inches or more, which is too limiting. Option E incorrectly states the height must be exactly 8 inches, disregarding the range of possible values.