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In the xy-plane, is the slope of line k equal to 0? (1) the

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by Brent@GMATPrepNow » Sat May 20, 2017 5:37 am
ziyuenlau wrote:In the xy-plane, is the slope of line k equal to 0?

(1) the x-intercept of k is 0
(2) the y-intercept of k is 0

Source : GMATPrep
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GREAT QUESTION!!

Target question: Is the slope of line k equal to 0?

Statement 1: The x-intercept of k is 0
This statement tells us two things:
- The line passes through the x-axis at the origin (0,0)
- The line CANNOT have slope of zero
Here's how we can draw the second conclusion: If line k were to have a slope equal to zero AND pass through (0,0), then the line would BE the x-axis, which means the line would have infinitely-many x-intercepts.
Since statement 1 tells us that the line does NOT have infinitely-many x-intercepts, we can be certain that the slope of line k IS NOT zero.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The y-intercept of k is 0
This tells us that the line passes through the y-axis at the origin (0,0)
There are infinitely many such lines.
Case a: the line passes through (0,0) and has slope zero
Case b: the line passes through (0,0) and has slope that is not zero
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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by [email protected] » Sat May 20, 2017 10:46 am
HI ziyuenlau,

This is a great 'concept' question - meaning that you don't really have to do any math to answer it as long as you understand the concepts involved. You might also find that drawing a few pictures based on the given information would help you to answer this question rather easily.

We're asked if Line K has a slope of 0. This question can be rewritten as "is Line K a horizontal line?" This is a YES/NO question.

1) THE X-intercept of K is 0

An X-intercept of a line is the ONE point that a line crosses the X-axis. This Fact means that Line K CANNOT be horizontal (if it were a horizontal line that passed through (0,0), then it would also pass through EVERY other point on the X-axis). Thus, Line K is NOT horizontal and the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

2) The Y-intercept of K is 0

A Y-intercept of a line is the ONE point that a line crosses the Y-axis. This Fact means that Line K COULD be horizontal, in which case the answer would be YES. But, Line K might also not be horizontal, in which case the answer would be NO.
Fact 2 is INSUFFICIENT

Final Answer: A

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by hazelnut01 » Sat May 20, 2017 7:00 pm
Brent@GMATPrepNow wrote:
ziyuenlau wrote:In the xy-plane, is the slope of line k equal to 0?

(1) the x-intercept of k is 0
(2) the y-intercept of k is 0

Source : GMATPrep
OA=A
GREAT QUESTION!!

Target question: Is the slope of line k equal to 0?

Statement 1: The x-intercept of k is 0
This statement tells us two things:
- The line passes through the x-axis at the origin (0,0)
- The line CANNOT have slope of zero
Here's how we can draw the second conclusion: If line k were to have a slope equal to zero AND pass through (0,0), then the line would BE the x-axis, which means the line would have infinitely-many x-intercepts.
Since statement 1 tells us that the line does NOT have infinitely-many x-intercepts, we can be certain that the slope of line k IS NOT zero.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The y-intercept of k is 0
This tells us that the line passes through the y-axis at the origin (0,0)
There are infinitely many such lines.
Case a: the line passes through (0,0) and has slope zero
Case b: the line passes through (0,0) and has slope that is not zero
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Hi Brent, Could you illustrate the graph for (1) & (2)?

y=mx+c

x-intercept is a point on the graph where y is zero. (x,0), mx+c=0
y-intercept is a point on the graph where x is zero. (0,y), y=c

Image

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by [email protected] » Sun May 21, 2017 11:03 am
Hi hazelnut01,

From your post, I think you understand the math concepts that this question is based on. You have to note the specific language that is used though - the prompt uses the phrases "THE X-intercept" and "THE Y-intercept", which means that there can only be ONE of each.

If a horizontal line passes through the Origin (0,0), then it has an INFINITE number of X-intercepts. That's NOT an option with Fact 1 though - it states that THE X-intercept is 0 (not "AN X-intercept is 0").

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