In the xy Plane, What is the Slope of Line l GMAT Data Sufficiency

Question: In the xy plane, what is the slope of line l?

1. Line l does not intersect the line with the equation y = 1 - x
2. Line l intersects the line with equation y = x - 1

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.

Correct Answer: A

Solution and Explanation:

Approach Solution 1:
(1) Line l does not intersect the line with the equation y = 1 – x

If the lines do not intersect in the xy- plane, then they are parallel. Parallel lines have the same slope, hence the slope of L = -1

Sufficient

(2) Line l intersects the line with the equation y = x – 1

There are infinitely many lines, with different slopes, which intersects with the line y = x – 1

Not sufficient

Approach Solution 2:
(1) Line l does not intersect the line with equation y = 1 - x.

Since line l does not intersect the line with equation y = 1-x, it is parallel to it.

Slope of line l = -1

SUFFICIENT

(2) Line l intersects the line with equation y = x – 1.

Since Line l intersects the line with equation y = x -1, it may have many slopes and can intersection the given line at many different points.
NOT SUFFICIENT

Approach Solution 3:
Given: In the xy-plane, lines k and l intersect at the point (1,1).

Target question: Is the y-intercept of k greater than the y-intercept of l?

Statement 1: The slope of k is less than the slope of l.

Let's examine 2 cases, and then make a generalization.

CASE A) the slope of line k is POSITIVE

For example, let's say line k has slope 1.

If line l has a greater slope (like a slope of 2), we can see that the y-intercept of k IS greater than the y-intercept of l

We can further see that if line l has a slope of 3, 4, 5, 6 etc , it will always be the case that the y-intercept of k IS greater than the y-intercept of l

CASE B) the slope of line k is NEGATIVE

For example, let's say line k has slope -1.5

If line l has a greater slope (like a slope of -0.6), we can see that the y-intercept of k IS greater than the y-intercept of l

We can further see that if line l has a slope that's greater than line k, it will always be the case that the y-intercept of k IS greater than the y-intercept of l

In both of the above cases, the answer to the target question will be the y-intercept of k IS greater than the y-intercept of l 00

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The slope of l is positive.

No information about line k

Statement 2 is NOT SUFFICIENT

“In the xy plane, what is the slope of line l?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". 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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