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: is \(m_1<m_2\)?

(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.

Graphic approach: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 (5,1)

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

The two statements individually are not sufficient.

(1)+(2) Note that

a higher absolute value of a slope indicates a steeper incline.

Now, if both lines have positive slopes then as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n:

Attachment:

1.PNG [ 14.29 KiB | Viewed 3046 times ]
If both lines have negative slopes then again as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line n is steeper hence the

absolute value of its slope is greater than the

absolute value of the slope of the line p, so the slope of n is

more negative than the slope of p, which means that the slope of p is greater than the slope of n:

Attachment:

2.PNG [ 13.66 KiB | Viewed 3045 times ]
So in both cases the slope of p is greater than the slope of n. Sufficient.

Answer: C.

For more on this topic check Coordinate Geometry Chapter of Math Book:

math-coordinate-geometry-87652.htmlHope it helps.

_________________

New to the Math Forum?

Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics