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# The number of students who attend a school could be divided

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Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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The number of students who attend a school could be divided [#permalink]  12 Aug 2018, 15:31
Expert's post
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Question Stats:

64% (00:53) correct 36% (00:42) wrong based on 25 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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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 128

Kudos [?]: 2046 [0], given: 397

Re: The number of students who attend a school could be divided [#permalink]  15 Aug 2018, 05:12
Expert's post
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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Sandy
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Joined: 13 Jul 2018
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GRE 1: Q159 V151
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Re: The number of students who attend a school could be divided [#permalink]  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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Joined: 02 Dec 2018
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Re: The number of students who attend a school could be divided [#permalink]  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.
Target Test Prep Representative
Joined: 12 Sep 2018
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Kudos [?]: 111 [2] , given: 0

Re: The number of students who attend a school could be divided [#permalink]  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.

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Re: The number of students who attend a school could be divided   [#permalink] 01 Feb 2019, 17:50
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