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At a bicycle shop, 60% of the bicycles are electric. How many of the bicycles are not electric?
(1) 31.25% of the electric bicycles are also mountain bikes.
(2) There are fewer than 200 bicycles at the shop.
(1) 31.25% of the electric bicycles are also mountain bikes.
(2) There are fewer than 200 bicycles at the shop.
28 Apr 2025, 14:12
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Official Solution:
At a bicycle shop, 60% of the bicycles are electric. How many of the bicycles are not electric?
Let the total number of bicycles be B. Then the number of electric bicycles is \(0.6 * B= \frac{3B}{5}\), and the number of non-electric bicycles is \(\frac{2B}{5}\). Since the number of electric bicycles must be an integer, B must be a multiple of 5. We are asked to find the number of non-electric bicycles, which is \(\frac{2B}{5}\).
(1) 31.25% of the electric bicycles are also mountain bikes.
Using the calculator, we can find that \(31.25\% = \frac{5}{16}\). Thus, the number of mountain bikes is \(\frac{5}{16} * \frac{3B}{5} = \frac{3B}{16}\). This implies that B must be a multiple of 16. From the stem, we know that B must also be a multiple of 5. Therefore, B must be a multiple of the least common multiple (LCM) of 5 and 16, which is 80. However, knowing only that B is a multiple of 80 is not enough to determine B. Not sufficient.
(2) There are fewer than 200 bicycles at the shop.
There are multiple values of B less than 200 that are divisible by 5, so this statement alone is not sufficient to determine B.
(1)+(2) From the above, B must be a multiple of 80 and less than 200. The possible values are 80 and 160. Since there is more than one possibility, the statements together are not sufficient.
Answer: E
At a bicycle shop, 60% of the bicycles are electric. How many of the bicycles are not electric?
Let the total number of bicycles be B. Then the number of electric bicycles is \(0.6 * B= \frac{3B}{5}\), and the number of non-electric bicycles is \(\frac{2B}{5}\). Since the number of electric bicycles must be an integer, B must be a multiple of 5. We are asked to find the number of non-electric bicycles, which is \(\frac{2B}{5}\).
(1) 31.25% of the electric bicycles are also mountain bikes.
Using the calculator, we can find that \(31.25\% = \frac{5}{16}\). Thus, the number of mountain bikes is \(\frac{5}{16} * \frac{3B}{5} = \frac{3B}{16}\). This implies that B must be a multiple of 16. From the stem, we know that B must also be a multiple of 5. Therefore, B must be a multiple of the least common multiple (LCM) of 5 and 16, which is 80. However, knowing only that B is a multiple of 80 is not enough to determine B. Not sufficient.
(2) There are fewer than 200 bicycles at the shop.
There are multiple values of B less than 200 that are divisible by 5, so this statement alone is not sufficient to determine B.
(1)+(2) From the above, B must be a multiple of 80 and less than 200. The possible values are 80 and 160. Since there is more than one possibility, the statements together are not sufficient.
Answer: E
