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
. 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
. Not sufficient.
(2) The y-intercept of line n
is greater than the y-intercept of line p
--> y-intercept is value of y
, so it's the value of b
. Not sufficient.
, 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
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:
1.PNG [ 14.29 KiB | Viewed 1990 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:
2.PNG [ 13.66 KiB | Viewed 1990 times ]
So in both cases the slope of p is greater than the slope of n. Sufficient.
For more on this topic check Coordinate Geometry Chapter of Math Book: math-coordinate-geometry-87652.html
Hope it helps.
NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;
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?
25 extra-hard Quant Tests
Get the best GMAT Prep Resources with GMAT Club Premium Membership