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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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Math Expert
Joined: 02 Sep 2009
Posts: 50585
If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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31 Oct 2018, 23:08
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55% (hard)

Question Stats:

56% (01:35) correct 44% (01:43) wrong based on 59 sessions

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

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

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Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 368
GMAT 1: 740 Q50 V40
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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31 Oct 2018, 23:29
Bunuel wrote:
If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?

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

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.

$$(n-1)[(n+3)-(n-2)] = m(n-1)$$
$$(n-1)5 = m(n-1)$$

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,
Math Expert
Joined: 02 Sep 2009
Posts: 50585
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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31 Oct 2018, 23:32
Bunuel wrote:
If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?

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

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.

$$(n-1)[(n+3)-(n-2)] = m(n-1)$$
$$(n-1)5 = m(n-1)$$

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,

________________________
It's m = 5. Edited. Thank you.
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Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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01 Nov 2018, 08:50
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
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Intern
Joined: 06 Oct 2018
Posts: 13
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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03 Nov 2018, 02:07

(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??

PS Forum Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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GMAT 1: 740 Q50 V40
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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03 Nov 2018, 02:14
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,

PierTotti17 wrote:

(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??

Intern
Joined: 06 Oct 2018
Posts: 13
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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03 Nov 2018, 02:38
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,

PierTotti17 wrote:

(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??

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.
Intern
Joined: 21 Oct 2018
Posts: 6
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n?  [#permalink]

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03 Nov 2018, 22:23
Hi Bunuel, why can't we cancel n-1 from both the sides, and solve from there?
Re: If (n + 3)(n − 1) − (n − 2)(n − 1) = m(n − 1), what is the value of n? &nbs [#permalink] 03 Nov 2018, 22:23
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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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