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The number of students who attend a school could be divided
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12 Aug 2018, 15:31
12 Aug 2018, 15:31
Expert Reply
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Question Stats:
79% (00:56) correct
20% (00:56) wrong based on 87 sessions
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The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. What is the minimum number of students that could attend the school?
(A) 120
(B) 160
(C) 240
(D) 320
(E) 480
(A) 120
(B) 160
(C) 240
(D) 320
(E) 480
Re: The number of students who attend a school could be divided
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15 Aug 2018, 05:12
15 Aug 2018, 05:12
Expert Reply
Explanation
The number of students must be divisible by 10, 12, and 16. So the question is really asking, “What is the least common multiple of 10, 12, and 16?” Since all of the answer choices end in 0, each is divisible by 10.
Just use the calculator to test which choices are also divisible by 12 and 16.
Because the question asks for the minimum, start by checking the smallest choices. Since \(\frac{120}{16}\) and \(\frac{160}{12}\) are not integers, the smallest choice that works is 240.
The number of students must be divisible by 10, 12, and 16. So the question is really asking, “What is the least common multiple of 10, 12, and 16?” Since all of the answer choices end in 0, each is divisible by 10.
Just use the calculator to test which choices are also divisible by 12 and 16.
Because the question asks for the minimum, start by checking the smallest choices. Since \(\frac{120}{16}\) and \(\frac{160}{12}\) are not integers, the smallest choice that works is 240.
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Re: The number of students who attend a school could be divided
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15 Aug 2018, 13:25
15 Aug 2018, 13:25
Factorise 10, 12, 16 and eliminate the repeated factors. What's left is the minimum number of students that could attend the school.
