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

It is currently 17 Nov 2018, 09:25

Gmatbusters' Weekly Quant Quiz

Join here 


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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     November 18, 2018

     November 18, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

If line k passes through the points (48, 33) and (31, 22),

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

Hide Tags

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 09 Jul 2018, 06:22
3
1
Top Contributor
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:53) correct 41% (02:49) wrong based on 78 sessions

HideShow timer Statistics

If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

*kudos for all correct solutions

_________________

Test confidently with gmatprepnow.com
Image

Most Helpful Expert Reply
MBA Section Director
User avatar
D
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 995
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 09 Jul 2018, 06:56
7
1
Since y-coordinate is 0 at which the line intercepts x-axis. Let (a,0) be the point where the the line meets x-axis.

Since (48,33), (31,22), (a,0) all lie on the same line, the slope calculated using any two of these points is equal

=> \(\frac{(33-22)}{(48-31)} = \frac{(22-0)}{(31-a)}\)

=> \(\frac{11}{17} = \frac{22}{(31-a)}\)

=> \(11 * (31-a) = 22 * 17\)

=> \(31 - a = 34\)

=> \(a = -3\)

Hence option B
_________________

If you like my post press kudos +1

New project wSTAT(which Schools To Apply To?)

New - RC Butler - 2 RC's everyday

General Discussion
Intern
Intern
User avatar
B
Joined: 17 May 2018
Posts: 38
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 09 Jul 2018, 06:50
2
2
If line passes through (31,22) and (48,33), it means that for every increase of 17 of x (48-31), y will increase by 11 (33-22). We want to know the value of x when y is zero so let's decrease y by 11 at a time, which will decrease x by 17 at a time. This means the line will pass through:
(31-17, 22-11) which is (14,11)
and
(14-17,11-11) which is (-3,0).

Answer is B
_________________

¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!

Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)
Premium Member
If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 09 Jul 2018, 07:35
1
GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

*kudos for all correct solutions


Equation of the line k passing through given vertices:
y-33=m(x-48)where m=11/17 (General form of equation of line passing through two points (x1,y1) and (x2,y2):- y-y1=m(x-x1)) and m=slope=(y2-y1)/(x2-x1)
At x intercept ,y=0. So,we have
-33=(11/17)(x-48)
Or, x-48=-51
Or, x=-51+48=-3 (please note this is the x-intecept point because we have determined x at y=0)

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Director
Director
User avatar
D
Joined: 11 Feb 2015
Posts: 565
Premium Member CAT Tests
If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post Updated on: 09 Jul 2018, 08:26
1
m (slope) = \(\frac{(y2 − y1)}{(x2 − x1)}\)

We have to determine the coordinate of the point where this line intercepts x-axis but the coordinate of y at this point is equal to 0.

Hence if we plug in the values of the two points as provided in the question stem & equate in the aforesaid formula we get the value of x intercept as -3

Hence option B is the correct answer.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"


Originally posted by CAMANISHPARMAR on 09 Jul 2018, 08:06.
Last edited by CAMANISHPARMAR on 09 Jul 2018, 08:26, edited 1 time in total.
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)
Premium Member
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 09 Jul 2018, 08:17
CAMANISHPARMAR wrote:
The "point-slope" form of the equation of a straight line is:

y2 − y1 = m(x2 − x1)

Therefore m = \(\frac{(y2 − y1)}{(x2 − x1)}\)

We have to determine the coordinate of the point where this line intercepts x-axis but the coordinate of y at this point is equal to 0.

Hence if we plug in the values of the two points as provided in the question stem & equate in the aforesaid formula we get the value of x intercept as -3

Hence option B is the correct answer.

Hi Manish,
Please check the equation of line in 2 point form .
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Director
Director
User avatar
D
Joined: 11 Feb 2015
Posts: 565
Premium Member CAT Tests
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 09 Jul 2018, 08:25
PKN wrote:
CAMANISHPARMAR wrote:
The "point-slope" form of the equation of a straight line is:

y2 − y1 = m(x2 − x1)

Therefore m = \(\frac{(y2 − y1)}{(x2 − x1)}\)

We have to determine the coordinate of the point where this line intercepts x-axis but the coordinate of y at this point is equal to 0.

Hence if we plug in the values of the two points as provided in the question stem & equate in the aforesaid formula we get the value of x intercept as -3

Hence option B is the correct answer.

Hi Manish,
Please check the equation of line in 2 point form .


Only the slope formula is required which is correct!
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2102
Premium Member CAT Tests
If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 10 Jul 2018, 10:33
2
GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

*kudos for all correct solutions

Shorter approaches are listed above. If those methods are unfamiliar and you know the slope-intercept equation of a line, the latter can be used without shortcuts to find the x-intercept.

Given: the line passes through points (48, 33) and (31, 22)

• Slope-intercept equation of a line: \(y=mx+b\)

\(m\) = slope and \(b\) = y-intercept. Find \(m\) and plug it into equation. Then find \(b\) and plug in. From that point find x-intercept.

• Slope = \(\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{33-22}{48-31}=\frac{11}{17}\)

Equation of the line with slope plugged in: \(y=\frac{11}{17}x+b\)

• To find \(b\), plug in (x,y) values from one coordinate. Using (31,22)

\(22=(\frac{11}{17}*31)+b\)
Clear the fraction*:
\((17*22)=(11*31)+17b\)
\((17*2*11) - (11*31)=17b\)
\(11(34-31)=17b\)
\(33=17b\)
\(b=\frac{33}{17}\)


Equation with \(b\) plugged in: \(y=\frac{11}{17}x+\frac{33}{17}\)

• x-intercept? Set y equal to 0 in the equation.

\(0=\frac{11}{17}x+\frac{33}{17}\)
\(0=11x+33\)
\(-33=11x\)
\(-\frac{33}{11}=x\)
\(-3=x\)


Answer B


*When clearing the fraction, do not do the multiplication.
Number sense: 11 can be factored out . . . Or that fact will be clear when 11 in one term is next to 22 in the other on LHS.
If numbers seem awkward and/or huge, often it is smarter to leave them factored.
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 11 Jul 2018, 07:02
1
Top Contributor
GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

*kudos for all correct solutions


If we sketch the two given points, we can quickly see that the slope (aka rise/run) of the line = 11/17
Image

So, we can use this information to plot another point on the line...
Image

And another point...
Image
..at which point, we can see that the x-intercept is -3

Answer: B

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

Show Tags

New post 14 Jul 2018, 18:31
GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11


We can let the x-intercept be a. Thus the coordinates of the x-intercept will be (a, 0). Since the x-intercept is on line k, the slope measured between the x-intercept and one of the two given points equals the slope measured between the two given points. Using the slope formula, we have:

(0 - 33)/(a - 48) = (22 - 33)/(31 - 48)

-33/(a - 48) = -11/(-17)

3/(a - 48) = 1/(-17)

a - 48 = -51

a = -3

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: If line k passes through the points (48, 33) and (31, 22), &nbs [#permalink] 14 Jul 2018, 18:31
Display posts from previous: Sort by

If line k passes through the points (48, 33) and (31, 22),

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


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®.