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# What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2)

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Math Expert
Joined: 02 Sep 2009
Posts: 46284
What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2) [#permalink]

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15 Sep 2017, 08:01
00:00

Difficulty:

35% (medium)

Question Stats:

71% (00:52) correct 29% (01:00) wrong based on 55 sessions

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What is the value of integer n ?

(1) (n – 2)(n + 2) = 5
(2) n(n + 2) = 15

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Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2) [#permalink]

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15 Sep 2017, 08:11
Find: n
Given : is an integer

(1) (n – 2)(n + 2) = 5
=> 5 = 1* 5 Or -1 * -5
=> (n – 2)(n + 2) = 1*5 => n=3
=> (n – 2)(n + 2) = -5 * -1 => n =-3
2 values of n => Insufficient

(2) n(n + 2) = 15
=> 15 = 1*15 or 3*5 or -5 * -3 => 1*15 will not make sense here so lets check for other 2 values.
For n to be integer
=> n(n+2) =3*5 => n=3
=> n(n+2) = -5 * -3 => n= -5
2 values of n => Insufficient

1+2
=> n=3

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Re: What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2) [#permalink]

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15 Sep 2017, 08:15
Bunuel wrote:
What is the value of integer n ?

(1) (n – 2)(n + 2) = 5
(2) n(n + 2) = 15

Stmt 1: n^2-4 = 5
n=+3 or -3 . Not definite . So insufficient.

Stmnt 2: n^2+2n-15=0;
n=+3 or n=-5 . Again not a feinite value for n; so insufficinet.

Combinin 1&2 n=+3; SO sufficient.
Ans:C
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Joined: 26 May 2017
Posts: 27
GMAT 1: 620 Q48 V27
Re: What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2) [#permalink]

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15 Sep 2017, 08:15
Bunuel wrote:
What is the value of integer n ?

(1) (n – 2)(n + 2) = 5
(2) n(n + 2) = 15

Statement 1:

(n+2)(n-2)=5 --> n2-4=5 --> n2=9 --> n= +3 or -3. Since we have two values of n, statement is not sufficient.

Statement 2:

n(n+2)=15 --> n2+2n-15=0 --> n2+5n-3n-15=0 --> n(n+5) -3(n+5)=0 --> (n+5) (n-3) = 0 --> n = 3 or -5. Since we have two values of n, statement is not sufficient.

Statement 1+2 gives us unique value of n=3. Hence C is the answer.

Manager
Joined: 12 Feb 2017
Posts: 71
Re: What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2) [#permalink]

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15 Sep 2017, 22:53
(1) (n – 2)(n + 2) = 5
n^2-4=5
n^2=9
n= +-3
Not sufficient.

(2) n(n + 2) = 15
n^2+2n-15=0
(n+5)(n-3)=0
n= -5 or n=3
Not sufficient.

Combining statements 1 and 2,
n=3.

Kudos if it helps.
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Re: What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2) [#permalink]

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16 Sep 2017, 19:47
Bunuel wrote:
What is the value of integer n ?

(1) (n – 2)(n + 2) = 5
(2) n(n + 2) = 15

1. (n – 2)(n + 2) = 5
=> n^2 - 4 = 5
=> n^2 = 9
=> n = 3 or -3

Not sufficient

(2) n(n + 2) = 15
=> n^2 +2n = 15
=> (n+5)(n-3) = 0
=> n = -5 or 3

Not sufficient

Combining 1 and 2 , we get
n=3
Sufficient

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Re: What is the value of integer n ? (1) (n – 2)(n + 2) = 5 (2) n(n + 2)   [#permalink] 16 Sep 2017, 19:47
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