GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 25 Mar 2019, 11:11

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.

Close

Request Expert Reply

Confirm Cancel

In the x-y coordinate plane, line k passes through the point (5, -4)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3522
Location: Canada
In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

Show Tags

New post 16 Oct 2018, 05:55
Top Contributor
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

44% (01:59) correct 56% (01:54) wrong based on 83 sessions

HideShow timer Statistics

In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only

_________________
Test confidently with gmatprepnow.com
Image
Manager
Manager
avatar
S
Joined: 04 Jun 2018
Posts: 157
GMAT 1: 610 Q48 V25
GMAT 2: 690 Q50 V32
GMAT 3: 710 Q50 V36
CAT Tests
Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

Show Tags

New post 16 Oct 2018, 06:33
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only





The answer should be equation 1 only.
By putting the value of (5,-4) in all the three equations, we can eliminate the 3rd equation.
SInce the x intercept is negative, equation 2 cannot be the answer. When we put x=0 in equation 2, x assumes a positive value.

SO equation 1 is the only correct.
SO answer should be Option A.
Intern
Intern
User avatar
B
Joined: 13 Mar 2018
Posts: 24
GPA: 3.12
WE: Project Management (Other)
Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

Show Tags

New post 16 Oct 2018, 06:35
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only


As per Question stem, X-intercept is negative. Hence put Y=0 in every equation to check if X-intercept is negative or not.
(I)> y=-0.4x-2 => Putting Y=0, we get - X intercept= NEGATIVE
(II)> y = 2 - 1.2x => Putting Y=0, we get -X intercept= POSITIVE
(III)> y = -0.7x - 1.5 => Putting Y=0, we get - X intercept= NEGATIVE

Hence, Statement (I) & (III) satisfies, this criteria i.e. X intercept is negative

Now Check whether point (5, -4) lies on these equations or not.
(I)> y=-0.4x-2 => Putting X=5 & Y=-4, Both LHS & RHS are equal, hence This point lies on this equation. Statement (I) satisfies.
(II)> y = 2 - 1.2x => Putting X=5 & Y=-4, Both LHS & RHS are equal, hence This point lies on this equation. Statement (II) satisfies.
(III)> y = -0.7x - 1.5 => Putting X=5 & Y=-4, Both LHS & RHS are not equal, hence This point doesn't lie on this equation. Statement (III) doesn't satisfies.

Hence, Statement (I) & (II) satisfies, this criteria i.e. point (5,-4) lies on the given line.

Taking both criteria into consideration, we get, only Statement (I) satisfies both the criteria. Hence, correct answer should be A.
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 911
Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

Show Tags

New post 16 Oct 2018, 12:18
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only

Reminder (to my students) / Suggestion (to the general reader):

1. One property at a time, till the end. Then the other. ("Don´t let your brain dance!")

2. Start with the easier checking property (or the one you feel more comfortable).
Indifferent? Start with the first.

\(?\,\,\left( 1 \right)\,\,\,\,:\,\,\,\,\left( {5, - 4} \right)\,\,\mathop \in \limits^? \,\,\,{\text{line}}\,\,\)

\(\left( i \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{2}{5}\left( 5 \right) - 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\)

\(\left( {ii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{6}{5}\left( 5 \right) + 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\)

\(\left( {iii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{7}{{10}}\left( 5 \right) - \frac{3}{2}\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( C \right),\,\,\left( E \right)\)


\(?\,\,\left( 2 \right)\,\,\,\,:\,\,\,\,{\text{line}}\,\,x - {\text{intercept}}\,\,\,\mathop < \limits^? \,\,0\)

\(\left( i \right)\,\,0\, = \,\, - \frac{2}{5}\left( x \right) - 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( B \right)\)

\(\left( {ii} \right)\,\,0\, = \,\, - \frac{6}{5}\left( x \right) + 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( D \right)\)


The correct answer is (A).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3522
Location: Canada
Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

Show Tags

New post 18 Oct 2018, 10:36
Top Contributor
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only


Notice that, if the line passes through the origin, then the line has slope -4/5 (aka a slope of -0.8), but the line will not have a negative x-intercept
Notice that, if the line passes through the (0,4), then the line will have slope 0, BUT the line will not have a negative x-intercept. See below.
Image

So, if the slope of the line is BETWEEN 0 and -0.8, then the line will have a negative x-intercept


Check the 3 statements:
i) y = -0.4x - 2
The slope = -0.4, which is BETWEEN 0 and -0.8. KEEP i for now

ii) y = 2 - 1.2x
Rewrite as: y = -1.2 + 2.
The slope = -1.2, which is NOT BETWEEN 0 and -0.8. So, ii cannot be true

iii) y = -0.7x - 1.5
The slope = -0.7, which is BETWEEN 0 and -0.8. KEEP iii for now

So far, i and iii COULD both be true.

However, in order for the point (5, -4) to be ON line k, its x and y coordinates must satisfy the equation of the line.
So, let's check i and iii

i) y = -0.4x - 2
Plug in x = 5 and y = -4 to get: -4 = -0.4(5) - 2 = -2 - 2 = -4
PERFECT!
So, i is true

iii) y = -0.7x - 1.5
Plug in x = 5 and y = -4 to get: -4 = -0.7(5) - 1.5 = -3.5 - 1.5 = -5
NO GOOD
So, iii is not true

Answer: A

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
Re: In the x-y coordinate plane, line k passes through the point (5, -4)   [#permalink] 18 Oct 2018, 10:36
Display posts from previous: Sort by

In the x-y coordinate plane, line k passes through the point (5, -4)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.