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Bunuel
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The number of students who attend a school could be divided among 10, [#permalink] New post  13 Aug 2018, 03:48
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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
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Abhishek009
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Re: The number of students who attend a school could be divided among 10, [#permalink] New post  13 Aug 2018, 06:45
Bunuel 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

LCM (16, 12, 10) = 240, Answer must be (C)
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Re: The number of students who attend a school could be divided among 10, [#permalink] New post  13 Aug 2018, 06:51
Bunuel 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 # of students is LCM of 10, 12 & 16, hence 240.

Answer C.


Thanks,
GyM
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BrentGMATPrepNow
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Re: The number of students who attend a school could be divided among 10, [#permalink] New post  05 Jan 2019, 08:23
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Bunuel 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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philipssonicare
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Re: The number of students who attend a school could be divided among 10, [#permalink] New post  27 Jan 2019, 22:00
This is a prime factorisation question.
https://www.mathsisfun.com/prime-factorization.html

\(10=5^1·2^1\)
\(12=2^2·3^1\)
\(16=2^4\)

So the lowest common multiple is \(2^4·3^1·5^1=\)
(C) 240
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KanishkM
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Re: The number of students who attend a school could be divided among 10, [#permalink] New post  27 Jan 2019, 22:49
Bunuel 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


LCM of 10, 12, or 16 buses, will give you the minimum number of students that could attend the school

C
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