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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

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by Gmat_mission » Sun Dec 26, 2021 2:23 pm

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Difficulty—

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

Answer: C

Source: Manhattan GMAT
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Re: The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports

by Brent@GMATPrepNow » Tue Dec 28, 2021 6:50 am
Gmat_mission wrote: ↑
Sun Dec 26, 2021 2:23 pm
 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

Answer: C

Source: Manhattan GMAT
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
Brent Hanneson - Creator of GMATPrepNow.com
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