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have a finite range

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have a finite range

by sanju09 » Sat Oct 03, 2009 1:58 am
Which of the following inequalities have a finite range of values of "x" satisfying them?
A. x^2 + 5 x + 6 > 0
B. |x + 2| > 4
C. 9 x - 7 < 3 x + 14
D. x^2 - 4 x + 3 < 0
E. (B) and (D)


[spoiler]The correct choice is (D) and the correct answer is x^2 - 4 x + 3 < 0.[/spoiler]
[spoiler]source: 4gmat.com[/spoiler]
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by cbenk121 » Mon Oct 05, 2009 12:55 pm
A is incorrect because infinitely many X's could satisfy x^2 + 5x > -6
B is incorrect because infinitely many X's could satisfy x+2 > 4 (even without absolute sign). This also means E is incorrect.
C is incorrect because infinitely many x's could satisfy x < 21/6
D by elimination is correct. However, logically you can see that x^2 - 4x < -3, which would be very tough to satisfy outside of a small range, since x^2 would quickly get larger than 4x.

Had a little difficulty understanding what "finite set" meant, at first I thought it meant there was a least one number that didn't satisfy equation, in which case all but (A) were correct...though x=-3 would cause A to be correct as well, because of the non-inclusive > than symbol.

Then realized it meant a set of X bounded on both sides by real numbers...thanks Wikipedia.
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by Stuart@KaplanGMAT » Mon Oct 05, 2009 2:38 pm
cbenk121 wrote:A is incorrect because infinitely many X's could satisfy x^2 + 5x > -6
B is incorrect because infinitely many X's could satisfy x+2 > 4 (even without absolute sign). This also means E is incorrect.
C is incorrect because infinitely many x's could satisfy x < 21/6
D by elimination is correct. However, logically you can see that x^2 - 4x < -3, which would be very tough to satisfy outside of a small range, since x^2 would quickly get larger than 4x.

Had a little difficulty understanding what "finite set" meant, at first I thought it meant there was a least one number that didn't satisfy equation, in which case all but (A) were correct...though x=-3 would cause A to be correct as well, because of the non-inclusive > than symbol.

Then realized it meant a set of X bounded on both sides by real numbers...thanks Wikipedia.
Excellent reasoning!

Your last point is very important as well. There are actually infinite possible values of x that satisfy all of the inequalities, which is why it's important to focus on the exact wording of the question: we don't need a finite number of values, we need a finite range of values, and only D satisfies that requirement.
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