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NathanMasky
Updated on: 19 Feb 2025, 15:19
Originally posted by NathanMasky on 19 Feb 2025, 15:05.
Last edited by NathanMasky on 19 Feb 2025, 15:19, edited 1 time in total.
Last edited by NathanMasky on 19 Feb 2025, 15:19, edited 1 time in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (02:41) correct
53%
(02:07)
wrong
based on 89
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During a carnival day a popcorn vendor sells 1/5 of its remaining popcorn, each hour without replenishment. What fraction of the original stock was sold, after 4 hours?
A. 1/625
B. 256/625
C. 61/125
D. 64/125
E. 369/625
A. 1/625
B. 256/625
C. 61/125
D. 64/125
E. 369/625
NathanMasky
19 Feb 2025, 15:06
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1. Calculate the fraction remaining after each hour:
Hour 1: The vendor sells 1/5, so 4/5 remains.
Hour 2: The vendor sells 1/5 of the remaining 4/5, which is (1/5) * (4/5) = 4/25. The fraction remaining is 4/5 - 4/25 = 16/25, or equivalently (4/5)*(4/5) = 16/25
Hour 3: The fraction remaining is (4/5) * (4/5) * (4/5) = 64/125
Hour 4: The fraction remaining is (4/5) * (4/5) * (4/5) * (4/5) = 256/625
2. Calculate the fraction sold:
Since 256/625 of the original stock remains after 4 hours, the fraction sold is:
1 - (256/625) = (625 - 256) / 625 = 369/625
Therefore, the answer is E. 369/625
Hour 1: The vendor sells 1/5, so 4/5 remains.
Hour 2: The vendor sells 1/5 of the remaining 4/5, which is (1/5) * (4/5) = 4/25. The fraction remaining is 4/5 - 4/25 = 16/25, or equivalently (4/5)*(4/5) = 16/25
Hour 3: The fraction remaining is (4/5) * (4/5) * (4/5) = 64/125
Hour 4: The fraction remaining is (4/5) * (4/5) * (4/5) * (4/5) = 256/625
2. Calculate the fraction sold:
Since 256/625 of the original stock remains after 4 hours, the fraction sold is:
1 - (256/625) = (625 - 256) / 625 = 369/625
Therefore, the answer is E. 369/625
20 Feb 2025, 01:53
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Looking at the answer choices and 1/5 in the question, let's assume the total original stock to be 625
Now 1/5th of the remaining stock get's sold each hour,
Fraction of original stock sold = 369/625
Answer E.
Now 1/5th of the remaining stock get's sold each hour,
| Hour | Sold | Remaining |
| 1 | 1/5*625 = 125 | 625-125 = 500 |
| 2 | 1/5*500 = 100 | 500-100 = 400 |
| 3 | 1/5*400 = 80 | 400-80 = 320 |
| 4 | 1/5*320 = 64 | No need to calc. |
| Total | 369 | No need to calc. |
Fraction of original stock sold = 369/625
Answer E.
