k = n^2 – 1

[Brent@GMATPrepNow]

If k and n are positive integers, and k = n^2 – 1, which of the following must be true?
I. k is not divisible by 5
II. nk divisible by 3
III. The units digit of k is not 7

(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

[sacx]

IMO A

the unit digit of n can be from 0 to 9. if you square any of these digits and then subtract 1 you will not get 7 in the units digit

[krisraam]

Answer is D

I. k is not divisible by 5. false. if n is 9. K is divisible by 5. Eliminate B,C,E.
II. nk divisible by 3.
nk = n(n-1)(n+1). These are 3 consecutive numbers. So one of them is 3. so nk is divisible by 3.

by now we know D is the answer by the process of elimination.

If you take 1 to 9. None of their squares has a unit digit 8.




If k and n are positive integers, and k = n^2 – 1, which of the following must be true?
I. k is not divisible by 5
II. nk divisible by 3
III. The units digit of k is not 7

(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

[Brent@GMATPrepNow]

Answer is D

I. k is not divisible by 5. false. if n is 9. K is divisible by 5. Eliminate B,C,E.
II. nk divisible by 3.
nk = n(n-1)(n+1). These are 3 consecutive numbers. So one of them is 3. so nk is divisible by 3.

by now we know D is the answer by the process of elimination.

If you take 1 to 9. None of their squares has a unit digit 8.

Nice work, krisraam
The answer is D


If k and n are positive integers, and k = n^2 – 1, which of the following must be true?
I. k is not divisible by 5
II. nk divisible by 3
III. The units digit of k is not 7

(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

[gaggleofgirls]

In the case of n=1, then K =0 so nk = 0

So what was keeping me between answer A and answer D was determining if 0/3.

0/3 = 0 Therefore the answer is D.

-Carrie

[mdavis]

How did you figure out that nk=n(n-1)(n+1) ?

[Brent@GMATPrepNow]

How did you figure out that nk=n(n-1)(n+1) ?

We know that k = n^2 - 1
We can factor n^2 - 1 to be (n+1)(n-1)
So, k = (n+1)(n-1)
nk = n(n+1)(n-1)

[krisraam]

Carie

n can't be 1 as when n is 1 k = n^2 -1 = 0 . K can't be 0 as n,k both are positive integers.

[gaggleofgirls]

Thanks for pointing that out, kris.

I noticed that for n to see if n could be 1 but didn't catch that it excludes n=1 since then k is not a pos int.

-Carrie