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After closing the restaurant, a chef calculates the total weight of the steaks served that day by rounding each steak's weight to the nearest 100 grams. Was the number of steaks served that day fewer than 25? (1 kilogram = 1,000 grams)
(1) The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms.
(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.
(1) The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms.
(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.
08 Jan 2025, 04:28
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Official Solution:
After closing the restaurant, a chef calculates the total weight of the steaks served that day by rounding each steak's weight to the nearest 100 grams. Was the number of steaks served that day fewer than 25? (1 kilogram = 1,000 grams)
Rounding each steak's weight to the nearest 100 grams means that if a steak weighed 480 grams, it would be rounded to 500 grams, and if it weighed 440 grams, it would be rounded to 400 grams. Note that the maximum difference between the rounded and actual weight of any steak is 50 grams. This occurs when the actual weight is exactly midway between two rounding points (e.g., 450 grams rounded to 500 grams, creating a difference of 50 grams).
(1) The difference between the total rounded weights and the total actual weights of the steaks was mote than 1.5 kilograms.
Since the maximum difference between the rounded and actual weights of any single steak is 50 grams, a total difference of 1.5 kilograms would require at least 1,500/50 = 30 steaks. This means that a difference of more than 1.5 kilograms would require more than 30 steaks, which is greater than 25. Sufficient.
(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.
This statement is clearly insufficient to determine whether fewer than 25 steaks were served. Not sufficient.
Answer: A
After closing the restaurant, a chef calculates the total weight of the steaks served that day by rounding each steak's weight to the nearest 100 grams. Was the number of steaks served that day fewer than 25? (1 kilogram = 1,000 grams)
Rounding each steak's weight to the nearest 100 grams means that if a steak weighed 480 grams, it would be rounded to 500 grams, and if it weighed 440 grams, it would be rounded to 400 grams. Note that the maximum difference between the rounded and actual weight of any steak is 50 grams. This occurs when the actual weight is exactly midway between two rounding points (e.g., 450 grams rounded to 500 grams, creating a difference of 50 grams).
(1) The difference between the total rounded weights and the total actual weights of the steaks was mote than 1.5 kilograms.
Since the maximum difference between the rounded and actual weights of any single steak is 50 grams, a total difference of 1.5 kilograms would require at least 1,500/50 = 30 steaks. This means that a difference of more than 1.5 kilograms would require more than 30 steaks, which is greater than 25. Sufficient.
(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.
This statement is clearly insufficient to determine whether fewer than 25 steaks were served. Not sufficient.
Answer: A
