IS (x+1)/(x-3) <0?
(1) -1<x<1
(2) X^2-4<0.
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Hi abhasjha,
For this DS question, we can TEST Values and/or use Number Properties. Here's how using Number Properties can help you to make quick work of this question...
We're asked if (X+1)/(X-3) < 0. This is a YES/NO question.
*Note, the only way to get a "YES" answer is if the numerator and denominator are DIFFERENT signs (one positive, one negative).
Fact 1: -1 < X < 1
With this restriction, we can make some quick deductions about the numerator and denominator:
The numerator WILL be POSITIVE (0 < numerator < 2).
The denominator WILL be NEGATIVE (-4 < denominator < -2)
Under these conditions, we will ALWAYS end up with a negative fraction, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
Fact 2: X^2 - 4 < 0
This gives us...
X^2 < 4
-2 < X < 2
Since this "range' of values includes the range from Fact 1, we know that we can get a YES answer.
IF....
-2 < X < -1 though, we end up with a NEGATIVE numerator AND a NEGATIVE denominator, which gives us a POSITIVE fraction. In this situation, the answer to the question is NO.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
For this DS question, we can TEST Values and/or use Number Properties. Here's how using Number Properties can help you to make quick work of this question...
We're asked if (X+1)/(X-3) < 0. This is a YES/NO question.
*Note, the only way to get a "YES" answer is if the numerator and denominator are DIFFERENT signs (one positive, one negative).
Fact 1: -1 < X < 1
With this restriction, we can make some quick deductions about the numerator and denominator:
The numerator WILL be POSITIVE (0 < numerator < 2).
The denominator WILL be NEGATIVE (-4 < denominator < -2)
Under these conditions, we will ALWAYS end up with a negative fraction, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
Fact 2: X^2 - 4 < 0
This gives us...
X^2 < 4
-2 < X < 2
Since this "range' of values includes the range from Fact 1, we know that we can get a YES answer.
IF....
-2 < X < -1 though, we end up with a NEGATIVE numerator AND a NEGATIVE denominator, which gives us a POSITIVE fraction. In this situation, the answer to the question is NO.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Determine the CRITICAL POINTS:abhasjha wrote:IS (x+1)/(x-3) <0?
(1) -1<x<1
(2) X^2-4<0.
The values of x where (x+1)/(x-3) is equal to 0 or is undefined.
(x+1)/(x-3) = 0 when x=-1.
(x+1)/(x-3) is undefined when x=3.
Thus, the critical points are x=-1 and x=3.
To determine where (x+1)/(x-3) < 0, test one value to the left and one value to the right of each critical point.
x<-1:
If x=-2, then (x+1)/(x-3) = (-2+1)/(-2-3) = 1/5.
Since (x+1)/(x-3) > 0 when x=-2, x<-1 is not a valid range.
-1<x<3:
If x=0, then (x+1)/(x-3) = (0+1)/(0-3) = -1/3.
Since (x+1)/(x-3) < 0 when x=0, -1<x<3 is a valid range.
x>3:
If x=4, then (x+1)/(x-3) = (4+1)/(4-3) = 5.
Since (x+1)/(x-3) > 0 when x=4, x>3 is not a valid range.
Thus, (x+1)/(x-3) < 0 when -1<x<3.
Question stem, rephrased:
Is -1<x<3?
Statement 1: -1<x<1
Thus, -1<x<3.
SUFFICIENT.
Statement 2: x²<4
If x=1, then -1<x<3.
If x=-1.5, then it is not true that -1<x<3.
INSUFFICIENT.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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