Question: Is (x – 2) (x – 3) > 0?
- x – 2 < 0
- x – 3 < 0
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.
Correct Answer: A
Solution and Explanation:
Approach Solution 1:
There is only one approach to solve this problem.
The given case scenario is to find whether (x – 2) (x – 3) > 0 is true or not and making use of the given two cases, it needs to be proved.
Based on case 1, it can be evaluated that-
when both (x – 2) and (x – 3) are +ve in eq (x – 2) (x – 3) > 0
Therefore it can be implied as
=> x>2 and x>3
By trying to plot the above values on the number line, it can be seen that the final equation comes out as-
Final equation will become x > 3
For the given 2nd case, it can be identified that when both (x – 2) and (x – 3) are -ve in eq (x – 2) (x – 3) > 0
Therefore =>x<2 and x<3
Again, by trying to plot the above values on the number line
Final equation will become x < 2
By summarising both the equations we see that either x > 3 or x < 2.
When we prove this through the given statements, it can be depicted as follows:
(1) x-2<0
which basically implies x <2.
Thus, the one that we need to prove is effectively true and sufficient considering the given question.
(2) x-3<0
Which mainly implies that, x < 3. Since nothing is given about x if it is an integer or not.
Hence x could be 2.5 or 1.5.
Accordingly,
if x=2.5 it will not satisfy x>3 or x<2
Further,
if x=1.5 it will satisfy x>3 or x<2
Hence Not Sufficient.
Therefore, the first statement x - 2 < 0 is only sufficient for the defining that (x – 2) (x – 3) > 0 is true.
“Is (x – 2) (x – 3) > 0?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
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