morbius14 wrote:A school administrator will assign each student in a group of n students to one of m classrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
(2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
Source: OG #135
I'm wondering if there is a systematic way to solving this question especially for evaluating statement 1.
Thanks!
To assign the same number of students to each classroom, the number of students (n) must be divisible by the number of classrooms (m).
Question rephrased:
Is n/m an integer?
Statement 1: It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
In other words, the number of students here (3n) is divisible by the number of classrooms (m), implying that 3n/m is an integer.
Since we need to determine whether m will always divide into n, plug in EXTREME values for m.
m=4:
It's possible that m=4 and n=16, with the result that 3n/m = (3*16)/4 = 12.
In this case, then n/m = 16/4 = 4, which is an integer.
m=12:
It's possible that m=12 and n=16, with the result that 3n/m = (3*16)/12 = 4.
In this case, n/m = 16/12 = 4/3, which is NOT an integer.
INSUFFICIENT.
Statement 2: It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
In other words, the number of students here (13n) is divisible by the number of classrooms (m), implying that 13n/m is an integer.
It is not possible that m divides into 13, since the only factors of 13 are 1 and 13, and m must be BETWEEN 3 and 13.
Thus, for 13n/m to be an integer, m must divide into n, implying that n/m is an integer.
SUFFICIENT.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
