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A gym class can be divided into 8 teams with an equal number

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A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96
[Reveal] Spoiler: OA
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New post 03 Dec 2012, 03:22
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96

The lowest possible number of students in the class will be the lowest common multiple of 8 and 12, which is 24.

Answer: B.
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Walkabout wrote:
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96




x/8 - integer
x/12- integer

24 divisible by both value( lowest possible number)
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Re: A gym class can be divided into 8 teams with an equal number [#permalink]

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New post 05 Jan 2015, 21:04
Walkabout wrote:
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96



it is not given that the teams must be of equal in number. why cant answer be 12+8 ?
any comments ??
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Re: A gym class can be divided into 8 teams with an equal number [#permalink]

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New post 05 Jan 2015, 21:27
gpitchuka wrote:
Walkabout wrote:
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96



it is not given that the teams must be of equal in number. why cant answer be 12+8 ?
any comments ??


A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

so the question does mention that
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Re: A gym class can be divided into 8 teams with an equal number [#permalink]

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New post 06 Jan 2015, 10:22
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Hi All,

This question is ultimately about finding the Least Common Multiple of 8 and 12. However, even if you did not realize that fact, the answer choices are numbers and we're asked to find the LEAST number of students that could be divided into 8 EQUAL teams OR 12 EQUAL teams. We can TEST THE ANSWERS until we find the match....

Let's start with the smallest and work our way up...

Answer A: 20 students. We CANNOT divide 20 students into 8 equal groups (you can't have "half a student"). Eliminate A.

Answer B: 24 students. We CAN divide 24 students into 8 groups of 3 OR 12 groups of 2. This FITS what we're looking for, so this MUST be the answer.

Final Answer:
[Reveal] Spoiler:
B


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Re: A gym class can be divided into 8 teams with an equal number [#permalink]

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New post 08 Jan 2015, 01:44
Just require to find the LCM of 8 & 12 = 24

Answer = B
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New post 15 Jun 2015, 13:24
I found the Lowest Common Multiple of 8 and 12 by prime factorization.
8=2^3
12=2^2*3

Now I took the highest power of each prime and multiplied them together.

2^3 *3= 24.
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Re: A gym class can be divided into 8 teams with an equal number [#permalink]

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New post 27 May 2016, 04:40
Walkabout wrote:
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96


We are given that a gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:

G/8 = integer and G/12 = integer

This means that G is a multiple of both 8 and 12.

We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.

Starting with 8, we have: 8, 16, 24, 32

For 12, we have: 12, 24

For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.

Answer B.
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Re: A gym class can be divided into 8 teams with an equal number [#permalink]

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New post 05 Jul 2016, 05:08
Walkabout wrote:
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

(A) 20
(B) 24
(C) 36
(D) 48
(E) 96



8*x=12*y

x=3 and y=2
8*3=12*2=24
Re: A gym class can be divided into 8 teams with an equal number   [#permalink] 05 Jul 2016, 05:08
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