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The number of students who attend a school could be divided

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The number of students who attend a school could be divided [#permalink] New post 12 Aug 2018, 15:31
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Question Stats:

78% (00:53) correct 21% (00:43) wrong based on 51 sessions
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
[Reveal] Spoiler: OA

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Joined: 07 Jun 2014
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Re: The number of students who attend a school could be divided [#permalink] New post 15 Aug 2018, 05:12
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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.
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Re: The number of students who attend a school could be divided [#permalink] New post 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.
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Re: The number of students who attend a school could be divided [#permalink] New post 02 Dec 2018, 08:21
Is it me or is this question ambiguous? The way I interpreted it is that the minimum number of students that could attend would be if there were 120 students divided into 10 buses.
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Re: The number of students who attend a school could be divided [#permalink] New post 01 Feb 2019, 17:50
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sandy wrote:
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

We need to determine the LCM of 10, 12, and 16

10 = 2 x 5

12 = 2^2 x 3

16 = 2^4

So the LCM is 2^4 x 3 x 5 = 16 x 3 x 5 = 240.

Answer: C
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Re: The number of students who attend a school could be divided [#permalink] New post 14 Aug 2020, 06:42
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sandy wrote:
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


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.
This tells us that the TOTAL number of students is a multiple of 10, 12 and 16

What is the minimum number of students that could attend the school?
This whole question is a clever way to ask "What is the LEAST common multiple of 10, 12, and 16?"

Since the answer choices are written is ASCENDING order, we can just start with answer choice A and keep checking answers until we find a value that is a multiple of 10, 12, and 16

(A) 120. This is NOT divisible by 16. ELIMINATE
(B) 160. This is NOT divisible by 12. ELIMINATE
(C) 240. This is divisible by 10, 12, and 16

Answer: C

Cheers,
Brent
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Re: The number of students who attend a school could be divided   [#permalink] 14 Aug 2020, 06:42
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