Hi Greg/All Day 4 : In the 2 month study plan, Day 4 Things to do section, in the Quant practice all previous concepts video, The last question, the answer can also be 36
If N is a positive intiger, and N^2 is divisible by 72 then the largest positive intiger that must divide N is
6, 12, 24, 36,48
Given answer - 12. This is the minimum value of N is 12. But it can also be 36 or 48. Please let me know if I’m missing something?
Since question is largest - answer must be 48. Link to video below.
“largest positive integer that must divide N” so not the value of N itself (which seems to be what you’re getting at).
Isn’t the largest positive integer which will divide N is N? Nx1 = N?
Sure, but that isn’t really related to what I was getting at.
Our question can be restated as follows:
For all positive integers N such that N^2 is divisible by 72, determine the largest integer M that divides every such N.
As you can surmise from first glance, N is generally not equal to M.
Indeed, N can be 36 or 48 because N^2 is a multiple of 72; however, M is not necessarily 36 or 48. For instance, if we let N = 24 then the “squared condition” (N^2 is a multiple of 72) is satisfied but 36 or 48 doesn’t divide 24, does it?
Just to iterate, if we have a set of all possible values of N then we’re looking to find the largest M such that it can divide every element in our set.