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# Is n negative? 1. (1 n ^ 2) < 0 2. n ^ 2 n 2 < 0

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VP
Joined: 05 Jul 2008
Posts: 1367
Is n negative? 1. (1 n ^ 2) < 0 2. n ^ 2 n 2 < 0 [#permalink]

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21 Jun 2009, 09:08
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Is n negative?

1. (1 – n ^ 2) < 0
2. n ^ 2 – n – 2 < 0

--== Message from GMAT Club Team ==--

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Senior Manager
Joined: 15 Jan 2008
Posts: 267

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21 Jun 2009, 22:35
1. N can be both positve ( >1) and negative ( <-1)
2. ( n-2)(n+1) < 0

All values for N between -1 and 2 satisifies.

Hence Ans E.

n can be positive or Negative.
Director
Joined: 04 Jan 2008
Posts: 859

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22 Jun 2009, 02:27
from (1), n can be +ve or -ve as n^2>1

from (2), -1<n<2

hence E
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Intern
Joined: 20 Apr 2008
Posts: 44

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22 Jun 2009, 02:41
I agree with Rooney

E is my choice
VP
Joined: 05 Jul 2008
Posts: 1367

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22 Jun 2009, 08:26
Its not A/B/D

What I did is

1. (1 – n ^ 2) < 0
2. n ^ 2 – n – 2 < 0

Added both the inequalities, which will give you -n-1 < 0

-1 < n means n > -1

So n can be -1/2 (-ve) or 1/2 (+ve) Hence E

Now the explanation from Knewton for C. Go here and look at the third problem So why is adding inequalities getting me to a diff answer. Is adding inequalities not permitted for quadratic equations?

http://www.knewton.com/gmat/tour/data_sufficiency

Statement 1 tells us that (1 – n2) < 0. We can add n2 to both sides of the inequality to get 1 < n2, or n2 > 1. If the square of a number is greater than 1, the number itself must either be greater than 1, or less than –1. For example, (–2)2 = 4. Since we do not know if n > 1 or n < –1, Statement 1 is insufficient. The answer must be B, C, or E.

Statement 2 tells us that n2 – n – 2 < 0. Since the expression on the right is quadratic, we should try to factor it. In this case, n2 – n – 2 = (n – 2)(n + 1), so we can rewrite the inequality as (n – 2)(n + 1) < 0. This tells us that the product of two expressions is less than zero. This can only be true if one of the expressions is positive and the other is negative. (n – 2) is positive if n > 2, zero if n = 2, and negative if n < 2. Similarly, (n + 1) is positive if n > –1, zero if n = –1, and negative if n < –1. We can figure out when the product of these two terms is negative by using a diagram:

Polynomial Diagram

By representing visually where each of the expressions is positive and negative, we can see more clearly that (n + 1)(n – 2) is negative when –1 < n < 2. In this region, (n + 1) is positive and (n – 2) is negative. Since we do not know if n is positive or negative, Statement 2 is also insufficient. The answer must be C or E.

Taken together, Statement 1 tells us that n > 1 or n < –1, and Statement 2 tells us that –1 < n < 2. The only overlap between these two regions is 1 < n < 2. Since 1 < n < 2, n must be positive. The answer to the question in the prompt is No. Since both statements together are sufficient to answer the question, answer choice C is correct.
Senior Manager
Joined: 16 Jan 2009
Posts: 349
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

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23 Jun 2009, 01:59
1. (1 – n ^ 2) < 0
n ^ 2 > 1

n can lie in the range except -1 to 1
n>1 OR n <-1

INSUFFICIENT.

2. n ^ 2 – n – 2 < 0
(n-2)(n+1)<0

either (n-2) is -ve or (n+1) is -ve both can not have the same sign.
either (n-2)<0 => n<2
or (n+1)<0 = >n<-1

INSUFFICIENT.

TOGETHER

from 1.
n>1 OR n <-1
from 2.
n<2 or n<-1

So n is -ve..
IMO C
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Lahoosaher

Manager
Joined: 16 Apr 2009
Posts: 219
Schools: Ross

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23 Jun 2009, 09:24
Good explanation, icandy.

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Re: DS question   [#permalink] 23 Jun 2009, 09:24
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