NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 14:47 It is currently 27 Apr 2024, 14:47
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

If the y-intercept of a line m is greater than 4, is the x-intercept

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
DHRJ0032
Manager
Manager
Joined: 27 Feb 2020
Posts: 108
Own Kudos [?]: 94 [5]
Given Kudos: 124
Location: India
Concentration: Finance, Operations
Schools: Owen '25 (II)
GPA: 4
WE:Operations (Aerospace and Defense)
Send PM
If the y-intercept of a line m is greater than 4, is the x-intercept [#permalink] New post   Updated on: 09 Aug 2021, 01:29
1
Kudos
4
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

51% (01:53) correct 49% (02:18) wrong based on 55 sessions
Hide Show timer Statistics
If the y-intercept of a line m is greater than 4, is the x-intercept of line m greater than 5 ?

(1) line m is perpendicular to the line n , y-2x-3=0.

(2) line m passes through (4,5) .
ShowHide Answer
Official Answer
A

Originally posted by DHRJ0032 on 08 Aug 2021, 07:59.
Last edited by Bunuel on 09 Aug 2021, 01:29, edited 1 time in total.
Renamed the topic and edited the question.
avatar
B
pk6969
Manager
Manager
Joined: 25 May 2020
Posts: 136
Own Kudos [?]: 13 [0]
Given Kudos: 70
Location: India
Concentration: Finance, General Management
Schools: Babson CBS '23 Broad
GPA: 3.2
Send PM
Re: If the y-intercept of a line m is greater than 4, is the x-intercept [#permalink] New post   08 Aug 2021, 10:59
DHRJ0032 wrote:
If the y-intercept of a line m is greater than 4, is the x-intercept of line m greater than 5 ?

1)line m is perpendicular to the line n , y-2x-3=0.

2)line m passes through (4,5) .


D.
1) since it is perpendicular, slope will be -1/m. So slope will be -1/2. so we have 4 values, slope, x1, x2, y1 and y2. we can calculate the intercept.
2) If we plot the point on graph we will see there is no way for slope to be less than 5.
Hence, D is answer.
User avatar
P
sj296
Senior Manager
Senior Manager
Joined: 09 Jul 2014
Posts: 371
Own Kudos [?]: 352 [1]
Given Kudos: 346
Location: India
Concentration: General Management, Finance
Schools: ISB '24
Send PM
Re: If the y-intercept of a line m is greater than 4, is the x-intercept [#permalink] New post   09 Aug 2021, 02:22
1
Kudos
Let's say the line 'm' is

y = px + C, where C is greater than 4 ........(1)

Statement 1:

Line 'm' is perpendicular to the line 'n', y - 2x - 3 = 0

=> y = 2x + 3

Since line m is perpendicular to line n, the slope of line m = -1/2 (the product of the slopes of two perpendicular lines = -1)

so eq (1) would become

y = (-1/2)x + C

to find x-intercept of the line m, put y = 0

x = -C*(-2) = 2C

Since C is greater than 4, 2C will be greater than 8. hence, x-intercept will be greater than 8.

So, we can say Yes, the x-intercept is greater than 5

Sufficient

Statement 2:

Line m passes through (4,5) & y-intercept is more than 4

This is an insufficient condition. Check the x-intercept of the line passing through (0, 4.5) & (4,5), and x-intercept of the line passing through (0,6) & (4,5)

Hence, OA should be A
avatar
B
pk6969
Manager
Manager
Joined: 25 May 2020
Posts: 136
Own Kudos [?]: 13 [0]
Given Kudos: 70
Location: India
Concentration: Finance, General Management
Schools: Babson CBS '23 Broad
GPA: 3.2
Send PM
Re: If the y-intercept of a line m is greater than 4, is the x-intercept [#permalink] New post   09 Aug 2021, 02:35
sj296 wrote:
Let's say the line 'm' is

y = px + C, where C is greater than 4 ........(1)

Statement 1:

Line 'm' is perpendicular to the line 'n', y - 2x - 3 = 0

=> y = 2x + 3

Since line m is perpendicular to line n, the slope of line m = -1/2 (the product of the slopes of two perpendicular lines = -1)

so eq (1) would become

y = (-1/2)x + C

to find x-intercept of the line m, put y = 0

x = -C*(-2) = 2C

Since C is greater than 4, 2C will be greater than 8. hence, x-intercept will be greater than 8.

So, we can say Yes, the x-intercept is greater than 5

Sufficient

Statement 2:

Line m passes through (4,5) & y-intercept is more than 4

This is an insufficient condition. Check the x-intercept of the line passing through (0, 4.5) & (4,5), and x-intercept of the line passing through (0,6) & (4,5)

Hence, OA should be A


Posted from my mobile device

In both the cases that you mentioned in statement 2, x intercept will be greater than 5. For more simplification, just plot those points on graph and you will see.
User avatar
P
sj296
Senior Manager
Senior Manager
Joined: 09 Jul 2014
Posts: 371
Own Kudos [?]: 352 [0]
Given Kudos: 346
Location: India
Concentration: General Management, Finance
Schools: ISB '24
Send PM
Re: If the y-intercept of a line m is greater than 4, is the x-intercept [#permalink] New post   09 Aug 2021, 03:06
pk6969 wrote:
sj296 wrote:
Let's say the line 'm' is

y = px + C, where C is greater than 4 ........(1)

Statement 1:

Line 'm' is perpendicular to the line 'n', y - 2x - 3 = 0

=> y = 2x + 3

Since line m is perpendicular to line n, the slope of line m = -1/2 (the product of the slopes of two perpendicular lines = -1)

so eq (1) would become

y = (-1/2)x + C

to find x-intercept of the line m, put y = 0

x = -C*(-2) = 2C

Since C is greater than 4, 2C will be greater than 8. hence, x-intercept will be greater than 8.

So, we can say Yes, the x-intercept is greater than 5

Sufficient

Statement 2:

Line m passes through (4,5) & y-intercept is more than 4

This is an insufficient condition. Check the x-intercept of the line passing through (0, 4.5) & (4,5), and x-intercept of the line passing through (0,6) & (4,5)

Hence, OA should be A


Posted from my mobile device

In both the cases that you mentioned in statement 2, x intercept will be greater than 5. For more simplification, just plot those points on graph and you will see.




Let's take two points

(0,4.5) and (4,5)

The line would be y = 0.125 x + 4.5

The x-intercept = -4.5/0.125 = -36

Let's take another set of two points (0,6) and (4,5)
the line would be y = 6-0.25x

the x-intercept = 24

You can also take y = 5 as well

Hence the statement 2 is not sufficient.

Hope you get what I am saying.
GMAT Club Bot
gmatclubot
Re: If the y-intercept of a line m is greater than 4, is the x-intercept [#permalink]
09 Aug 2021, 03:06
Moderator:
Bunuel
Math Expert
92959 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