Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jun 0911:00 AM IST
-01:00 PM IST
Attend this session to evaluate your current skill level, learn process skills, and solve through tough Arithmetic questions
Jun 1105:40 AM PDT
-12:00 PM PDT
Register for the GMAT Club Virtual MBA Spotlight fair, the biggest MBA fair of the year. You will have a chance to hear Admissions directors from almost every Top 20 program speak, network with peers, and more.
Jun 1111:00 AM PDT
-12:00 PM PDT
Magoosh students get into top business schools like MIT Sloan, HBS, Stanford GSB, Wharton and more! See why over 6 million students trust us for exam prep.
Jun 1310:00 AM EDT
-10:30 AM EDT
Level up your Chicago Booth MBA application! Sia Admissions will be LIVE on June 13th for expert guidance on crafting your application that resonates with admission committees. Learn core themes, personal branding tips, and strategies and more.
Jun 1311:00 AM EDT
-12:00 PM EDT
TTP has received over 700 reviews on GMAT Club! This incredible milestone is a testament to our dedication to helping students score high on the GMAT for over a decade.
Jun 1412:00 PM EDT
-01:00 PM EDT
Have you ever wondered how to score a PERFECT 805 on the GMAT Focus Edition? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
A line passes through (1,p), is its slope greater than 0?
[#permalink]
16 Jan 2023, 10:32
16 Jan 2023, 10:32
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
85%
(hard)
Question Stats:
41% (02:51) correct
59%
(02:31)
wrong
based on 22
sessions
A line passes through (1,p), is its slope greater than 0?
(1) The line passes through (p,13)
(2) The line passes through (p,-1)
(1) The line passes through (p,13)
(2) The line passes through (p,-1)
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3130
Given Kudos: 1857
Location: India
Concentration: Strategy, Leadership
A line passes through (1,p), is its slope greater than 0?
[#permalink]
17 Jan 2023, 01:58
17 Jan 2023, 01:58
1
Kudos
Bunuel wrote:
gmatophobia wrote:
Bunuel wrote:
A line passes through (1,p), is its slope greater than 0?
(1) The line passes through (p,13)
(2) The line passes through (p,-1)
(1) The line passes through (p,13)
(2) The line passes through (p,-1)
Statement 1
(1) The line passes through (p,13)
Slope =\(\frac{ y_2 - y_1 }{ x_2 - x_1}\) = \(\frac{13 - p }{ p - 1}\)
For certain values of p, the slope is greater than 0. For p = 13, the slope = 0
The statement is not sufficient.
Statement 2
(2) The line passes through (p,-1)
Slope =\(\frac{ y_2 - y_1 }{ x_2 - x_1}\) = \(\frac{ -1-p }{ p - 1}\)
For certain values of p, the slope is greater than 0. For p = -1, the slope = 0
The statement is not sufficient.
Combined
The statements combined
\(\frac{ -1-p }{ p - 1}\) = \(\frac{13 - p }{ p - 1}\)
Solving we can get an unique value of p. Sufficient.
Option C
And what would that solution be? Is the slope greater than 0?
(p-1)(-1-p) = (p-1)(13-p)
(p-1)[-1-p -13 +p] = 0
(p-1) * -14 = 0
p = 1
The slope is undefined.
In fact we can see this behavior using the statements as well. For the same value of p (i.e. x coordinate), the line has two different values of y coordinate. Hence the line is parallel to Y axis.
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3130
Given Kudos: 1857
Location: India
Concentration: Strategy, Leadership
Re: A line passes through (1,p), is its slope greater than 0?
[#permalink]
16 Jan 2023, 14:30
16 Jan 2023, 14:30
Bunuel wrote:
A line passes through (1,p), is its slope greater than 0?
(1) The line passes through (p,13)
(2) The line passes through (p,-1)
(1) The line passes through (p,13)
(2) The line passes through (p,-1)
Statement 1
(1) The line passes through (p,13)
Slope =\(\frac{ y_2 - y_1 }{ x_2 - x_1}\) = \(\frac{13 - p }{ p - 1}\)
For certain values of p, the slope is greater than 0. For p = 13, the slope = 0
The statement is not sufficient.
Statement 2
(2) The line passes through (p,-1)
Slope =\(\frac{ y_2 - y_1 }{ x_2 - x_1}\) = \(\frac{ -1-p }{ p - 1}\)
For certain values of p, the slope is greater than 0. For p = -1, the slope = 0
The statement is not sufficient.
Combined
The statements combined
\(\frac{ -1-p }{ p - 1}\) = \(\frac{13 - p }{ p - 1}\)
Solving we can get an unique value of p. Sufficient.
Option C
