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Statement 1 and 2 are not sufficient by their own.

Attachment:
Soln.jpeg
Soln.jpeg [ 143.12 KiB | Viewed 5622 times ]

Option C is the correct Answer
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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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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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chetan2u,

So the question becomes do the lines need to be in the same direction? How do we know that?
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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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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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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.

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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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?

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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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

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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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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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

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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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.
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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pdfff
    avigutman sir can you help me with this problem
Happy to, pdfff. Why don't you first walk me through your thinking, so I can better assist you.
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