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

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:

GMAT assassins aren't born, they're made,
Rich

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.

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.

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

Just require to find the LCM of 8 & 12 = 24

Answer = B

8*x=12*y

x=3 and y=2
8*3=12*2=24

4*3*2=24 which is divisible by 2 or8 if ?/x= we assume lest either may 2 or 3 so we go throug an option 24/3=8 ,24/2=12

Posted from my mobile device

Total no. of students= x

x= 8k = 2^3 *k (k is a positive integer)
x= 12a = 2^2*3*a (a is a positive integer)

LCM= 2^3*3= 24

The value could change depending on the value of k and a but this will be the least value. All other values will now be a multiple of 24.

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