NEW HERE? LEARN MORE
closeclose
Last visit was: 13 May 2024, 23:50 It is currently 13 May 2024, 23:50
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A line passes through (1,p), is its slope greater than 0?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93245
Own Kudos [?]: 623570 [0]
Given Kudos: 81851
Send PM
CAT Tests Forum Quiz Mode
A line passes through (1,p), is its slope greater than 0? [#permalink] New post   16 Jan 2023, 10:32
Expert Reply
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

41% (02:51) correct 59% (02:31) wrong based on 22 sessions
Hide Show timer Statistics
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)
ShowHide Answer
Official Answer
C
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3124
Own Kudos [?]: 4354 [0]
Given Kudos: 1853
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: A line passes through (1,p), is its slope greater than 0? [#permalink] New post   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)


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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93245
Own Kudos [?]: 623570 [0]
Given Kudos: 81851
Send PM
CAT Tests Forum Quiz Mode
Re: A line passes through (1,p), is its slope greater than 0? [#permalink] New post   17 Jan 2023, 01:39
Expert Reply
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)


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?
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3124
Own Kudos [?]: 4354 [1]
Given Kudos: 1853
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
A line passes through (1,p), is its slope greater than 0? [#permalink] New post   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)


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.
GMAT Club Bot
gmatclubot
A line passes through (1,p), is its slope greater than 0? [#permalink]
17 Jan 2023, 01:58
Moderator:
Bunuel
Math Expert
93244 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions