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16 Aug 2019, 02:11
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B
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:
40% (02:33) correct
60%
(02:25)
wrong
based on 75
sessions
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A regional shipping facility has received a cars, each of which must be distributed to one of b dealerships in the region. If 3 < b< 7 and a > 7, is it possible to distribute the a cars to the b dealerships such that each dealership receives the same number of cars?
(1) It would be possible to distribute 3a cars that each dealership receives the same number of cars.
(2) It would be possible to distribute 7a cars that each dealership receives the same number of cars.
(1) It would be possible to distribute 3a cars that each dealership receives the same number of cars.
(2) It would be possible to distribute 7a cars that each dealership receives the same number of cars.
16 Aug 2019, 02:14
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17 Sep 2019, 23:32
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Official Explanation
This "distributing evenly" business will boil down to divisibility. For example, if there are 5 dealerships, we'll be able to distribute the cars evenly if the number of cars is divisible by 5. On to the data statements, separately first.
Statement (1) tells us that we could distribute 3a cars. This whole business is ripe for analysis by cases, because there are only a few possible numbers of dealerships: the number of dealerships is b = 4, 5, or 6. We'll start with b = 4 and a = 8, so 3a = 24 Those numbers all fit the conditions in the question and Statement (1), so it's a legal case. We can distribute 24 cars evenly to 4 dealership. Can we distribute a cars evenly? Since a = 8, we could, and the answer is yes. That's Case I. We'll try to find a case in which the answer is no. Perhaps b = 5 and a = 8? That's not a legal case, because 3a = 24 cars can't be distributed equally among 5 dealerships. We notice a pattern. The statement is telling us that
3a/b = integer
But b must be 4, 5, or 6. With the 3 present, is the only way 3a/b will be an integer that b goes into a? No, wait: b could be 6 and a could possess a factor of 2. If a = 10, b = 6, 3a cars could be divided evenly among the 6 dealerships, but not a cars. We have obtained a valid case with an answer "no," so Statement (1) is insufficient.
Statement (2) is similar. It says that
7a/b = integer
This time we draw a different conclusion. Since b must be 4, 5, or 6, and none of those numbers goes into 7, b must go into a. That means each of b dealerships can receive an equal share of a cars, and the answer to the question is definitively "yes." Statement (2) is sufficient.
The correct answer is (B).
