Lines n and p lie in xy plane

[shibal]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p

oa C

[ssuarezo]

We could calculate the slope for y=4 and y=5 as examples (one greater than the other):

line n: (1-4)/(5-0) = -4/5
line l: (1-5)/(5-0) = -1

so just by having the relation between y-intercepts and the common point, we can find the answer, in summary: C

[pops]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p

oa C

statement 1. Insufficient as point of intersection doesn't talks anything about the slope.

statement 2. y-intercept doesn't make things clear. may be y intercept of line n is greater but this does not mean its slope is greater as its x intercept also might be bigger.

1&2 combined can answer since once we get an intersection point it acts as hinge. So more the y-intercept more is the slope.

p.s. question should be in data sufficiency section.

[rah_pandey]

The only importance of first statement is that it tells that n and p are not parallel(slope not same). if the original question included one more statement that n and P are not parallel than in that case B would have been correct irrespective of point of intersection.

Rahul

[sidceg]

If one has a positive slope or zero slope (parallel to X axis)and another has a negative slope, does it mean the slope of the second one is lesser than the first one?

[[email protected]]

Hi sidceg,

Yes. Since lines can be written in Slope-Intercept 'format' (Y = MX + B), you have a way to compare the slopes of two lines. If the first line has a positive or 0 value for 'M' and the second line has a negative value for 'M', then the second value IS less than the first.

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
(1) Lines n and p intersect at (5, 1)
(2) the y-intercept of line n is greater than the y-intercept of line p

Target question: Is slope of line n less than slope of line p?

Statement 1: Lines n and p intersect at (5, 1)
We can use sketches to show that statement (1) is NOT SUFFICIENT



Statement 2: the y-intercept of line n is greater than the y-intercept of line p
We can use sketches to show that statement (2) is NOT SUFFIENT.


Statements 1 and 2 combined
Let n be the y-intercept of line n
Let p be the y-intercept of line p.

So, line n has the points (0,n) and (5,1).
And line p has the points (0,p) and (5,1)

IMPORTANT: We also know that n>p (from statement 2)

When we apply the slope formula, we get:
Slope of line n = (1-n)/(5-0)= (1-n)/5
Slope of line p = (1-p)/(5-0)= (1-p)/5
Since n>p, we know that (1-p)/5 (the slope of line p) WILL BE GREATER than (1-n)/5 (the slope of line n)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

[didieravoaka]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
(1) Lines n and p intersect at (5, 1)
(2) the y-intercept of line n is greater than the y-intercept of line p

Target question: Is slope of line n less than slope of line p?

Statement 1: Lines n and p intersect at (5, 1)
We can use sketches to show that statement (1) is NOT SUFFICIENT



Statement 2: the y-intercept of line n is greater than the y-intercept of line p
We can use sketches to show that statement (2) is NOT SUFFIENT.


Statements 1 and 2 combined
Let n be the y-intercept of line n
Let p be the y-intercept of line p.

So, line n has the points (0,n) and (5,1).
And line p has the points (0,p) and (5,1)

IMPORTANT: We also know that n>p (from statement 2)

When we apply the slope formula, we get:
Slope of line n = (1-n)/(5-0)= (1-n)/5
Slope of line p = (1-p)/(5-0)= (1-p)/5
Since n>p, we know that (1-p)/5 (the slope of line p) WILL BE GREATER than (1-n)/5 (the slope of line n)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent,

I have some issues to determine the slopes could you show me how you ended up with those slopes?
Thanks.

[Brent@GMATPrepNow]

Brent,

I have some issues to determine the slopes could you show me how you ended up with those slopes?
Thanks.

Here's a free video on slopes - https://www.gmatprepnow.com/module/gmat- ... /video/995

Also, here's one on horizontal and vertical lines - https://www.gmatprepnow.com/module/gmat- ... /video/994

Let me know if you have any questions afterwards.

Cheers,
Brent

[GMATinsight]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p

oa C

Answer: Option C

[Jeff@TargetTestPrep]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?

1) Lines n and p intersect at (5, 1)

2) Y-intercept of line n is greater than y intercept of line p

We need to determine whether the slope of line n is less than the slope of line p.

Statement One Alone:

Lines n and p intersect at the point (5,1).

If the two lines intersect at a point, they are not parallel and hence their slopes are not equal (unless they are identical lines). So the slope of one line must be greater than the slope of the other line. However, we can't determine which line has the greater slope. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

The y-intercept of line n is greater than the y-intercept of line p.

Knowing that the y-intercept of one line is greater than the y-intercept of the other does not allow us to determine which line has the greater slope.

For example, line n could have a y-intercept 2 and slope 3, and line p could have a y-intercept 1 and slope 2. In this case, line p has the lesser slope. However, it's also possible that line n could have a y-intercept 2 and slope 2, and line p could have a y-intercept 1 and slope 3. In which case, line n has the lesser slope. Statement two alone is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Knowing the point where the two lines intersect and the relationship of the y-intercept of each line allows us to determine which line has the lesser slope.

Even though we don't know the actual y-intercept of each line, we know that the y-intercept of line n is greater than that of line p. So we can let the y-intercept of line n be b, and that of line p be c where b > c.

Thus, line n passes through (0, b), and line p passes through (0, c). Both lines also pass through (5, 1). Let's calculate their slopes:

Slope of line n = (1 - b)/(5 - 0) = (1 - b)/5

Slope of line p = (1 - c)/(5 - 0) = (1 - c)/5

Now let's determine whether (1 - b)/5 < (1 - c)/5.

Is (1 - b)/5 < (1 - c)/5 ?

Is 1 - b < 1 - c ?

Is -b < -c ?

Is b > c ?

Since, from the information in statement two, we know that b is greater than c, we have answered the question: the slope of line n is indeed less than that of line p.

Answer: C