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.

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

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

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