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Lines n and p lie in the xy-plane. Is the slope of line n less than th 16 May 2018, 06:11
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aaronhew
If you try to gauge the difficulty of this question, would it be a 400-level question, 500-level, 600-level, etc?

Coordinate plane questions tend to be most difficult for me right now. I'm working on my ability to solve these types. So, it would be helpful to be able to gauge the degree of difficulty for problems that trouble me.
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This question is fairly difficult.

Given me a chance to rate this question, I would rate it as 700 difficulty level question. Although every question on GMAT CLUB has difficulty level tagged in it.
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 11 Jun 2018, 23:49
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BANON
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.
Show more


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

There can be infinite lines passing through (5,1), we don't know which are lines n & p. Hence we cannot answer the question about their slopes.

Statement 1 alone is Not Sufficient.

Statement 2:
The y-intercept of line n is greater than the y-intercept of line p

The lines can be passing through any quadrant, irrespective of how their y intercepts compare to each other, hence their slopes will vary.

Statement 2 alone is not Sufficient.

Combining the 2 statements.
We have. Two specific lines, passing through point (5,1), with y intercept of one greater than the other.
This is enough information to imagine their slopes.

Combing the 2 statements is Sufficient.

Answer C.


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Lines n and p lie in the xy-plane. Is the slope of line n less than th 02 Jun 2019, 22:01
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Statement 1 alone clearly is insufficient as either of the lines can have a higher slope if they intersect at (5,1)...Strike off A and D

Statement 2 alone also is insufficient as if y intercept of one line is greater, that tells nothing about the slope as the 2 lines may be parallel or may intersect on the left side or the right side of y axis. Hence Strike of B too

Statement 1 and 2 together definitely will suffice to find which line has a higher slope as the one which has larger y intercept will have a bigger slope (-y/x). Hence Answer is C
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 03 Jun 2019, 00:30
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Statement 1 and 2 are not sufficient by their own.

Attachment:
Soln.jpeg
Soln.jpeg [ 143.12 KiB | Viewed 5301 times ]

Option C is the correct Answer
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 13 Oct 2019, 21:28
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3 conditions:
both slopes are positive: Kp>Kn>0
both slopes are negative: Kn<Kp<0
slope of line n is negative and slope of line p is positive: Kn<0<Kp

the slope of n is less than the slope of p (Kn<Kp) in all the three conditions.
Thus, choose C
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 27 Nov 2019, 21:15
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Hi chetan2u

I see that there are two groups in the above discussion.
I am part of the group that still believes E is the answer.

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

For example, y-intercept of line n is 6
y-intercept of line P is -19

But if line n can be a downward sloping line while line P could be upward sloping.
In that case, Line P will not have have less slope than Line N?
What am I missing here?
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 27 Nov 2019, 21:22
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chetan2u,

So the question becomes do the lines need to be in the same direction? How do we know that?
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 29 Nov 2019, 17:51
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Hello @VeritasKarishma- do the lines need to be in the same direction? How do we know that?

I think I am missing something here.
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 25 Dec 2019, 23:37
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I agree with you, I have similar doubt and had marked E. Experts please clarify ,by algebra it is coming C as @Bunnel did it right but by Graph approach answer is coming E.

akash7gupta11
Hello @VeritasKarishma- do the lines need to be in the same direction? How do we know that?

I think I am missing something here.
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Lines n and p lie in the xy-plane. Is the slope of line n less than th Updated on: 10 Nov 2020, 07:33
Originally posted by BrentGMATPrepNow on 29 Apr 2020, 10:25.
Last edited by BrentGMATPrepNow on 10 Nov 2020, 07:33, edited 1 time in total.
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BANON
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.
Show more

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
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 29 Apr 2020, 15:07
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BoundMan
Hi chetan2u

I see that there are two groups in the above discussion.
I am part of the group that still believes E is the answer.

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

For example, y-intercept of line n is 6
y-intercept of line P is -19

But if line n can be a downward sloping line while line P could be upward sloping.
In that case, Line P will not have have less slope than Line N?
What am I missing here?
Show more

Your test case in red is accurate. Slope of P will be > Slope of N in this test case mentioned in red

In every other test case, taking into account both S1 and S2 -- it always turns out the slope of P > Slope of N

Given the answer is consistently, slope of P > Slope of N in every test case .. the answer to the question [Is the slope of line n less than the slope of line p ?] is consistently in every test case "No"

Hence, s1 and s2 together are sufficient to answer the question
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 28 Apr 2021, 15:10
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GMATinsight
BANON
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.


Answer: Option C

Check the cases as per color coding
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For the combined case, why can't we easily switch the n and p pink lines? To me you can get 2 different answers and it should be E.
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 27 May 2021, 01:45
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VeritasKarishma Please check the final answer and tell me where went wrong. As other posts are saying that slope of n < slope of p

statement 1:
passing via (5,1)

line n 1=5m1+n
line p 1=5m2+p

Statement 2:
n>p

1+2


m1= 1-n/5
m2 = 1-p/5

both 5 gets canceled

1- n and 1-p
n>p

let n=3 p=2
1-3 and 1-2
-2 and -1
m1=2 and m2=1
m1>m2
slope of n>slope of P
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 27 May 2021, 04:44
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BharatTj
VeritasKarishma Please check the final answer and tell me where went wrong. As other posts are saying that slope of n < slope of p

statement 1:
passing via (5,1)

line n 1=5m1+n
line p 1=5m2+p

Statement 2:
n>p

1+2


m1= 1-n/5
m2 = 1-p/5

both 5 gets canceled

1- n and 1-p
n>p

let n=3 p=2
1-3 and 1-2
-2 and -1
m1=2 and m2=1
m1>m2
slope of n>slope of P
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If n > p, then -n < -p (multiplying by -1 on both sides will flip the inequality)
Then ( 1- n) < (1 - p) (adding 1 to both sides does not change the inequality sign)
So slope of N < Slope of P
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 18 Nov 2022, 11:06
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Bunuel
BANON
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

Algebraic approach:

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

We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?

(1) Lines n and p intersect at the point (5,1) --> \(1=5m_1+b_1=5m_2+b_2\) --> \(5(m_1-m_2)=b_2-b_1\). Not sufficient.

(2) The y-intercept of line \(n\) is greater than the y-intercept of line \(p\) --> y-intercept is value of \(y\) for \(x=0\), so it's the value of \(b\) --> \(b_1>b_2\) or \(b_2-b_1<0\). Not sufficient.

(1)+(2) \(5(m_1-m_2)=b_2-b_1\), as from (2) \(b_2-b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1-m_2)<0\) --> \(m_1-m_2<0\) --> \(m_1<m_2\). Sufficient.

Answer: C.

For more on this topic check Coordinate Geometry Chapter of Math Book: https://gmatclub.com/forum/math-coordina ... 87652.html

Hope it helps.
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Bunuel
I ended up using smart numbers

Let's say for line n that b =6 and for line p that b=4

Line n --> y=mx+6

Line p --> y=mx+4

I then plugged in the point (5,1) to find the slope of each equation

Line n's equation ends up being --> y=-x+6
Line p's equation ends up being --> y=-3/5x+4

So, the slope of line n is less than the slope of line p.

Is this an okay approach, or did I just stumble upon the answer?
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    avigutman sir can you help me with this problem
BANON
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.
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Lines n and p lie in the xy-plane. Is the slope of line n less than th 03 Jun 2023, 16:29
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pdfff
    avigutman sir can you help me with this problem
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Happy to, pdfff. Why don't you first walk me through your thinking, so I can better assist you.
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