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On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?
(1) Point P has an x-value of 1 and is 2 units away from the origin
(2) The line does not pass through Quadrant IV
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
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On the x-y coordinate grid, does the line passing through point P (not...
Steps 1 & 2: Understand Question and Draw Inferences
To find whether the slope is greater than 2, you need information on the orientation of the line. This can come from two points of the line or at least one point that the line passes above or below.
Step 3: Analyze Statement 1
(1) Point P has an x-value of 1 and is 2 units away from the origin
Statement 1 tells you that from the origin, point P creates a right triangle. Use the Pythagorean Theorem to find the y-value: (The triangle base is the x-value of 1, the hypotenuse is the distance of 2, and the height is the y-value)
The height of the triangle, which is the y-value of point p, has an absolute value of √3, making it either √3 or –√3. However, you need two points to draw the line, and you don’t know whether point P is in quadrant I or IV.
Statement 1 is not sufficient.
Step 4: Analyze Statement 2
(2) The line does not pass through Quadrant IV
Statement 2 tells you that the slope is positive (to avoid Quadrant IV), but you don’t know whether it’s greater than 2.
Statement 2 is not sufficient.
Step 5: Analyze Both Statements Together (if needed)
From statement 1, you know the (x, y) values of point P are either (1, √3) or (1, –√3), placing point P in either Quadrant I or IV.
From statement 2, you know that point P is in Quadrant I. You also know the line cannot cross into Quadrant IV.
As shown above, the slope is√3. The line can rotate clockwise, making the slope less, but it cannot rotate counterclockwise, as that would bring it into Quadrant IV. Taken together, you know that the slope is not greater than 2.
Statements 1 and 2 together are sufficient.
Answer: Option (C)
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On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?
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On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On the x-y coordinate grid, does the line passing through point P (not shown) have a slope greater than 2?(1)Point P has an x-value of 1 and is 2 units away from the origin(2)The line does not pass through Quadrant IVa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
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