If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?

Question

(1) |m| = 5
(2) m = 5

Gladiator59 · Answer

Hi  Bunuel , The statement 2 seems to be incomplete. Please check!

(n+3)(n-1) - (n-2)(n-1) = m(n-1)

On first look,  (n-1)  seems to be common through out.

(n-1)  = m(n-1) 
 (n-1)5 = m(n-1)

Hence,

n-1 = 0   OR   m =5 .

Hence we need one of these two conditions to be true for the equation to hold.

Best Regards,
Gladi

Bunuel · Answer

________________________
It's m = 5. Edited. Thank you.

nkin · Answer

We can simplify question to:
(n-1)(n+3-n+2) = m(n-1)
(n-1)*5 = m*(n-1)
m*(n-1) - 5*(n-1) = 0
(m-5)*(n-1) = 0 ............. (A)

Now, stmt 1: |m| = 5, i.e. m=5, or m = -5
If m = 5, then (A) becomes 0*(n-1) = 0, so n can be any value. 
If m = -5, then (A) becomes -10*(n-1) = 0 or n = 1
Hence insufficient. Eliminate A,D

Now, stmt 2: m = 5, similar to above, (A) becomes 0*(n-1) = 0, so n can be any value. 
Hence Insufficient. Eliminate B

Now, Combined, we get the condition, m = 5, again (A) becomes 0*(n-1) = 0, so n can be any value. 
Hence insufficient. Eliminate C.

So as per my analysis, answer should be  Option E

PierTotti17 · Answer

I am getting answer B. Someone please help

(n+3)(n-1) - (n-2)(n-1) = m(n-1) (n^2+2n-3) - (n^2-3n+2) = m(n-1) (n^2+2n-3) - n^2+3n-2 =mn-m 5n-5 = mn-m 5(n-1) = m(n-1) m=5 Stmnt 1) Mod m = 5 --> m=5 or -5 since m=5 m can't be -5, hence insufficient. Stmnt 2) m=5 sufficient?? Someone please explain. Made a mistake in simplifying question stem?

Gladiator59 · Answer

Hi  PierTotti17 ,

You have simplified the stem correctly and arrived at the correct conclusion. For the expression to be true m has to be 5. But the question is asking for the value of n. Once m is 5 we cannot acertain the value of n as it could be anything and still the expression would be true. Plug in values of n=1 and n=10 to see this... Hence we cannot answer the question with st1 and st2 both.

So option (E) is the answer.

Let me know if this makes sense.

Best,
Gladi

PierTotti17 · Answer

And that's what happens when you skim the question: you look like a muppet. Thanks Gladiator for pointing out where I was going wrong.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards