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rishab1988
- Master | Next Rank: 500 Posts
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Inequalities
Source: Beat The GMAT — Data Sufficiency |
Statement 1: (1 - n²) < 0rishab1988 wrote:Is n negative?
1) [1-(n^2)] <0
2) n^2-n-2<0
Implies n² > 1 => Either n < -1 or n > 1
Not sufficient.
Statement 2: (n² - n - 2) < 0
Implies (n - 2)(n + 1) < 0 => -1 < n < 2
Not sufficient.
1 & 2 Together: Combining both of the inequalities we get only acceptable region of values is 1 < n < 2. Thus n is not negative.
Sufficient.
The correct answer is C.
Note: Combining both the inequalities means n must satisfy both of them. Thus the possible region of values for n is the intersection of the both regions.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
rishab1988
- Master | Next Rank: 500 Posts
- Posts: 332
- Thanked: 41 times
- GMAT Score:720
Rahul.Seems I made a mistake in statement 2.
I interpreted it as (x-2)(x+1)<0
Therefore, either x-2 <0 -> x<2 or x+1<0 -> x<-1
So,should it not be x<2 or x<-1
Please shed some more light on this issue.I treated statement 2 in the same way as I did 1
I interpreted it as (x-2)(x+1)<0
Therefore, either x-2 <0 -> x<2 or x+1<0 -> x<-1
So,should it not be x<2 or x<-1
Please shed some more light on this issue.I treated statement 2 in the same way as I did 1
Careful!rishab1988 wrote:Rahul.Seems I made a mistake in statement 2.
I interpreted it as (x-2)(x+1)<0
Therefore, either x-2 <0 -> x<2 or x+1<0 -> x<-1
So,should it not be x<2 or x<-1
Please shed some more light on this issue.I treated statement 2 in the same way as I did 1
When you are saying x < -1, then x is also less than 2. Thus the product becomes positive.
In this kind of cases, draw a number line, mark the critical points (here -1 and 2) on it and try to see which region satisfies the inequality by picking some easy integers (like 0) and plugging it into the inequality.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
rishab1988
- Master | Next Rank: 500 Posts
- Posts: 332
- Thanked: 41 times
- GMAT Score:720
brilliant!Rahul@gurome wrote:Careful!rishab1988 wrote:Rahul.Seems I made a mistake in statement 2.
I interpreted it as (x-2)(x+1)<0
Therefore, either x-2 <0 -> x<2 or x+1<0 -> x<-1
So,should it not be x<2 or x<-1
Please shed some more light on this issue.I treated statement 2 in the same way as I did 1
When you are saying x < -1, then x is also less than 2. Thus the product becomes positive.
In this kind of cases, draw a number line, mark the critical points (here -1 and 2) on it and try to see which region satisfies the inequality by picking some easy integers (like 0) and plugging it into the inequality.
You solved the problem.I will keep these points in mind.
