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# The number of students who attend a school could be divided among 10,

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Joined: 02 Sep 2009
Posts: 55681
The number of students who attend a school could be divided among 10,  [#permalink]

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13 Aug 2018, 04:48
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Difficulty:

25% (medium)

Question Stats:

72% (01:14) correct 28% (01:29) wrong based on 159 sessions

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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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Re: The number of students who attend a school could be divided among 10,  [#permalink]

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13 Aug 2018, 07:45
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]

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13 Aug 2018, 07:51
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.

Thanks,
GyM
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Re: The number of students who attend a school could be divided among 10,  [#permalink]

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05 Jan 2019, 09:23
Top Contributor
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

Cheers,
Brent
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Re: The number of students who attend a school could be divided among 10,  [#permalink]

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27 Jan 2019, 23:00
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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Re: The number of students who attend a school could be divided among 10,  [#permalink]

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27 Jan 2019, 23:49
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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Re: The number of students who attend a school could be divided among 10,   [#permalink] 27 Jan 2019, 23:49
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