N is an integer
Quantity A
the largest integer that must divide by n^3-n
Quantity B
the largest integer that must divide n^3- 3n^2-+2n
Resource target test prep.
My question is I tried to apply choosing #s strategy by choosing zero, answer is C and 10 answer is A, So answer is D. BUT the right answer is C. I asked one of TTP tutors and he told me that choosing #s strategy doesn’t work here.
Any thoughts Geeks?
could you reformat the question problem, can’t seem to understand it.
what about Now?
I’m assuming your question is
given n is an integer
Quantity A: largest integer that must divide n^3-n
Quantity B: largest integer that must divide n^3 - 3n^2 + 2n
First step would be to simply both the equations
Quantity A: n(n^2 - 1) = n(n - 1)(n + 1)
Quantity B: n(n^2 -3n + 2) = n(n - 2)(n - 1)
let’s choose 0
Quantity A: 0
Quantity B: 0
therefore the larget integer that will divide both the quantities is \infty answer choice C
let’s choose 1
Quantity A: 1(1 -1)(1+1) = 0
Quantity B: 1(1 - 2)(1 - 1) = 0
therefore the larget integer that will divide both the quantities is \infty answer choice C
let’s choose -1
Quantity A: -1(-1 -1)(-1+1) = 0
Quantity B: -1(-1 - 2)(-1 - 1) = -6
therefore the larget integer that will divide quantity A is \infty and quantity B is 6 answer choice A
So in my view the answer should be D.
But if you just look at the quantities
Quantity A: n(n - 1)(n + 1)
Quantity B: n(n - 2)(n - 1)
then the largest integer for quantity A will be n + 1 and for quantity B will be n which makes the answer A.
So either there is something wrong with the question or there is a mistake in my calculation.
@gregmat could you take a look at my calculation once.
Thank you for your solution, I have the same concern because I used the process that you followed.
@gregmat Need you to help please.
right answer is C Not D
Can you make sure that you’re copying the question exactly as written? The original question was hard for me to parse. Can you check the source again and make sure it’s copied precisely the same?
Here ya guys go! I made a short video. Hopefully this clears up any doubts
what is the exact form of this expression, 2-+2n, is it minus or plus after 2? super confused
It has to be n^3-3n^2+2n because that’s factorable
but if the quantity A is 24 and quantity B is 6 then the max integer that can divide quantity A is 24 and quantity B is 6 right ? because the question doesn’t talk about the max integer that can divide both the numbers simultaneously.
I’m definitely doing something wrong in my mind
Because we are dealing with the expression, not a specific case.
this is right, but we are looking at QA, QB separately. For QA, 
24 can be a divisor of 0, but is not a divisor of 6
oh got it basically we’ve to find the largest integer that will divide all of the numbers that we got from quantity A.
