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The number of students who attend a school could be divided

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1601 [0], given: 373

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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:

30% (01:00) correct 70% (00:47) wrong based on 10 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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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1601 [0], given: 373

CAT Tests
Re: The number of students who attend a school could be divided [#permalink] New post 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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Joined: 13 Jul 2018
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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.
Re: The number of students who attend a school could be divided   [#permalink] 15 Aug 2018, 13:25
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