Is (x + 1)/(x - 3) < 0 ?

‘Is (x + 1)/(x - 3) < 0 ? ’ is.a topic for GMAT Quantitative Reasoning. GMAT quantitative reasoning section analyses the candidates' ability to solve quantitative problems and interpret graphic data. This section of the GMAT exam comprises 31 questions that need to be completed in 62 minutes. This topic is the GMAT Quantitative Reasoning question that comes with five options. Candidates need to choose the one which is correct. GMAT Quant syllabus has mainly the two categories-

• Problem Solving: This question type in GMAT Quantitative Reasoning candidates logical and analytical reasoning skills. In this section, candidates indicate the best five answer choices.
• Data Sufficiency: Candidates' ability to analyse quantitative Reasoning problems and identify relevance with the data given.

Topic - Is (x + 1)/(x - 3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

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Answer: A

Model Answer 1

Explanation - The question formatting can be done this way-
Is (x+1)/(x-3)<0 ?
= \(\frac{x+1}{x-3}\) <0
This means roots are -1 and 3
so 3 ranges will be x<−1, −13
Let us check the extreme value
if xx some very large number then
=\(\frac{x+1}{x-3}\) =\(\frac{positive}{positive}\)> 0

Expression is positive in the third range, then turns negative in the second and turns positive once again in the first: + - +. In this case, the range is −1 Thus, the fundamental query is: −1 In statement 1
-1 < x < 1 which is sufficient
In statement 21
x^2 - 4 < 0
= -2 < x < 2 which is insufficient
So the answer is A, which is Statement 1 is sufficient , but statement 2 is not sufficient.

Model Answer 2

Explanation - There is another way to Solve this question-
So let's examine the question's specifics. If the ratio of the two quantities is negative, then neither the numerator nor the denominator may be positive at the same time.
Let us look at statement 1
Because x is larger than -1, the numerator will be positive. Since the greatest value of x is very near to 1, the denominator will always be negative since subtracting 3 from it will get a negative integer. Thus, we arrive to a bad conclusion. SUFFICIENT.
Let us look at statement 2
Because the MAX x obtained is extremely near to 2, which means the denominator will once more always be negative. The numerator can now, however, be either positive [for x>-1] or negative [for -2 x-1]. As a result, the outcome may be either favourable or negative. NOT SUFFICIENT.
So the answer is A, which is Statement 1 is sufficient , but statement 2 is not sufficient.