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25 Sep 2025, 02:39
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Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1.: Yes
Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2.: Yes
Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37.: Yes
Samira is comparing 10 compact car models. She has two preferences about their fuel efficiency:
1. The city mileage should be at least 28 miles per gallon (mpg).
2. The highway mileage should be at most 38 mpg.
For each of the following statements, select Yes if it accurately reflects the information provided. Otherwise, select No.
1. The city mileage should be at least 28 miles per gallon (mpg).
2. The highway mileage should be at most 38 mpg.
| Car | City mpg | Highway mpg |
|---|---|---|
| A | 26 | 37 |
| B | 29 | 40 |
| C | 32 | 36 |
| D | 27 | 39 |
| E | 30 | 35 |
| F | 31 | 41 |
| G | 28 | 34 |
| H | 33 | 37 |
| I | 25 | 36 |
| J | 30 | 38 |
For each of the following statements, select Yes if it accurately reflects the information provided. Otherwise, select No.
| Yes | No | |
| Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1. | ||
| Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2. | ||
| Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37. |
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Official Answer
Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1.: Yes
Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2.: Yes
Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37.: Yes
25 Sep 2025, 02:39
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Official Solution:
• Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1.
The cars that satisfy Preference 2 (highway mpg ≤ 38) are A, C, E, G, H, I, and J. The lowest city mpg among these is 25, which is car I, and that value is below 28, so it fails Preference 1 (city mpg ≥ 28).
Answer: Yes
• Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2.
The cars that satisfy Preference 1 (city mpg ≥ 28) are B, C, E, F, G, H, and J. The maximum highway mpg among these is 41, which is car F, and that value is above 38, so it fails Preference 2 (highway mpg ≤ 38).
Answer: Yes
• Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37.
First identify the sets. Preference 1 includes B, C, E, F, G, H, and J. Preference 2 includes A, C, E, G, H, I, and J. Exactly one preference means cars that are in one set but not the other. This gives the group A, B, F, and I. Their highway mpg values are 37 for A, 40 for B, 41 for F, and 36 for I. Only A has a highway mpg of 37. Car H also has a highway mpg of 37 but it is excluded because it satisfies both preferences.
Answer: Yes
Correct answer:
Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1. "Yes"
Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2. "Yes"
Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37. "Yes"
bb
• Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1.
The cars that satisfy Preference 2 (highway mpg ≤ 38) are A, C, E, G, H, I, and J. The lowest city mpg among these is 25, which is car I, and that value is below 28, so it fails Preference 1 (city mpg ≥ 28).
Answer: Yes
• Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2.
The cars that satisfy Preference 1 (city mpg ≥ 28) are B, C, E, F, G, H, and J. The maximum highway mpg among these is 41, which is car F, and that value is above 38, so it fails Preference 2 (highway mpg ≤ 38).
Answer: Yes
• Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37.
First identify the sets. Preference 1 includes B, C, E, F, G, H, and J. Preference 2 includes A, C, E, G, H, I, and J. Exactly one preference means cars that are in one set but not the other. This gives the group A, B, F, and I. Their highway mpg values are 37 for A, 40 for B, 41 for F, and 36 for I. Only A has a highway mpg of 37. Car H also has a highway mpg of 37 but it is excluded because it satisfies both preferences.
Answer: Yes
Correct answer:
Among cars that satisfy Preference 2, the lowest city mpg belongs to a car that fails Preference 1. "Yes"
Among cars that satisfy Preference 1, the maximum highway mpg is achieved by a car that fails Preference 2. "Yes"
Among cars that satisfy exactly one of the two preferences, exactly one car has highway mpg equal to 37. "Yes"
26 Feb 2026, 06:24
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Honestly speaking a straightforward reference question. Just depends on how quick you can arrange according to ur need. Sort it in decending or ascending depending on the the constraints makes it easier to visualise.
