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

It is currently 16 Oct 2019, 19:54

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 coordinate plane, points (x, 1) and (10, y) are on line k. If

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 74
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Reviews Badge
In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 03 May 2013, 18:43
3
7
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:45) correct 22% (02:22) wrong based on 213 sessions

HideShow timer Statistics

In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12

_________________
If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 04 May 2013, 04:46
5
4
Most Helpful Community Reply
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 590
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 17 Nov 2013, 22:41
3
2
avohden wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes
through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12


As both the points are on the same line, and the line passes through the origin with a positive slope,
\(\frac{1-0}{x-0} = \frac{1}{2}\) and \(\frac{y-0}{10-0} = \frac{1}{2}\)

Hence, x=2 and y=5

Thus, x+y = 7

B.

IMO more like 550.
_________________
General Discussion
MBA Section Director
User avatar
V
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 7105
City: Pune
GMAT ToolKit User
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 04 May 2013, 07:52
4
1
We know the equation of any line is y=mx+c

Where m = slope and c = y intercept (point where line crosses y axis)

Since line passes thru origin then y intercept (i.e. C) must be zero

we also know m = slope = 1/2

so the equation becomes y=\(\frac{x}{2}\)

we are given two points that are on line (x,1) (10,y)

Plug second point (10,y) in to the equation y=\(\frac{10}{2}\) --------> y=5

Plug First point (x,1) in to the equation 1=\(\frac{x}{2}\) -----------> x=2

x+y = 7

Choice B

Regards,

Narenn
_________________
2020 MBA Applicants: Introduce Yourself Here!

MBA Video Series - Video answers to specific components and questions about MBA applications.

2020 MBA Deadlines, Essay Questions and Analysis of all top MBA programs
Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 20
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 04 May 2013, 11:02
manishuol wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12


Equation of a line passing through origin and having a slope m is given by \(y = mx\)

Hence the equation of the given line is \(y = 0.5 * x\)

This gives the values of x and y as 2 and 5 respectively.
Hence x + y = 7

Correct Answer is B
Manager
Manager
avatar
Joined: 24 Apr 2013
Posts: 51
Location: United States
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 21 Oct 2013, 11:18
My approach was to apply the rise/run=slope rule

so,

y-1/10-x = 1/2
2y-2=10-x
2y+x=12, substitute with one of the given points (x,1)
2(1) +x=12, x=10, y=1, x+y=11

can someone please tell me why this approach doesn't work?
_________________
Struggling: make or break attempt
MBA Section Director
User avatar
V
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 7105
City: Pune
GMAT ToolKit User
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 21 Oct 2013, 11:40
SaraLotfy wrote:
My approach was to apply the rise/run=slope rule

so,

y-1/10-x = 1/2
2y-2=10-x
2y+x=12, substitute with one of the given points (x,1)
2(1) +x=12, x=10, y=1, x+y=11

can someone please tell me why this approach doesn't work?


IMO what you have obtained (2y+x=12) is the algebraic equation, but it is not the equation of a line.

Equation of line is described as y=mx+c ------> where 'm' is the slope of a line and 'c' is the 'y' intercept.

Per the equation 2y+x=12

\(m=slope=-\frac{1}{2}\) (which is not correct. The slope is \(\frac{1}{2}\))

c=y intercept = 6 (This is also not correct. We know that line is passing thru origin, so its y intercept (the y value of point where line crosses 'y' axis) must be zero.
_________________
2020 MBA Applicants: Introduce Yourself Here!

MBA Video Series - Video answers to specific components and questions about MBA applications.

2020 MBA Deadlines, Essay Questions and Analysis of all top MBA programs
Senior Manager
Senior Manager
User avatar
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 475
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 20 Nov 2013, 17:43
1

Official Explanation


Answer: B We're given the slope of a line and one point on the line (the origin: 0,0). From this, we can determine every other point on the line. The most direct way to find x and y involves solving for each individually.

We know that slope (1/2, in this case), is equal to the change in y divided by the change in x. Since we know that the line passes through (0,0) and (x,1), we can solve as follows:

1/2 = (1 – 0)/(x – 0)
1/2 = 1/x
x = 2

Use the same approach to solve for y:

1/2 = (y – 0)/(10 – 0)
1/2 = y/10
y = 5

Thus, x + y = 2 + 5 = 7, choice (B).
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1571
Concentration: Finance
GMAT ToolKit User
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 28 Dec 2013, 09:16
1
mau5 wrote:
avohden wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes
through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12


As both the points are on the same line, and the line passes through the origin with a positive slope,
\(\frac{1-0}{x-0} = \frac{1}{2}\) and \(\frac{y-0}{10-0} = \frac{1}{2}\)

Hence, x=2 and y=5

Thus, x+y = 7

B.

IMO more like 550.


One can only check the coordiantes and solve

See, we are given that y = 1/2x

So first coordinate since y =1 then x = 2
Second coordinate since x = 1= then y=5

So add em up 2+5 = 7

B

Hope its clear

Cheers
J :)
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 26 May 2015, 21:52
Hi All,

This question has a great "brute force" element to it. Since we know that the line passes through the Origin (0,0) and has a slope of 1/2, we can "map out" as many co-ordinates as we need to to answer the given question.

Since the slope is 1/2, for every increase of 2 in the X-coordinate we have an increase of 1 in the Y-coordinate:

(0,0)
(2,1)
(4,2)
(6,3)
(8,4)
(10, 5)

We're told that (X,1) and (10,Y) are on the line. We're asked for the value of X+Y....

From our list of co-ordinates, we can see that X = 2 and Y = 5...

X+Y = 2+5 = 7

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Retired Moderator
avatar
V
Joined: 22 Jun 2014
Posts: 1093
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 27 May 2016, 07:29
Slope m = (y2 - y1) / (x2 - x1) ---formula equation

there are three points on the line (0,0) , (x,1) and (10,y).

given m = 1/2.

first take (0,0) , (x,1) and m=1/2 and put these in formula equation and we get
1/2 = 1-0 / x-0 hence x=2

first take (0,0) , (10,y) and m=1/2 and put these in formula equation and we get
1/2 = y-0 / 10-0 hence y=5

x+y = 5+2 = 7.
_________________
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1230
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 14 Feb 2018, 12:52
manishuol wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12



Hi niks18 :) please let me know if my solution/ approach is correct ? :)


\(\frac{1-y}{x-10}=\frac{1}{2}\) cross multiply

\(2-2y = x-10\)

\(x-10-2+2y\)

\(x+2y-12 = 0\)

\(2y= 12-x\)

\(y = \frac{-x}{2}+ 6\)

now since I know that slop is \(1/2\) hence x = 1 and y intercept is 6

so x+y = 1+6 = 7

Answer: 7 <---- :)

many thanks! :)
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 15 Feb 2018, 03:14
1
dave13 wrote:
manishuol wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12



Hi niks18 :) please let me know if my solution/ approach is correct ? :)


\(\frac{1-y}{x-10}=\frac{1}{2}\) cross multiply

\(2-2y = x-10\)

\(x-10-2+2y\)

\(x+2y-12 = 0\)

\(2y= 12-x\)

\(y = \frac{-x}{2}+ 6\)

now since I know that slop is \(1/2\) hence x = 1 and y intercept is 6


so x+y = 1+6 = 7

Answer: 7 <---- :)

many thanks! :)


Hi dave13,

what you have done is used the formula to find slope and converted it to an algebraic equation which does not represent the equation of line.

equation of line is \(y=mx+c\), where \(m\) is slope of the line

as per your equation \(y=\frac{-1}{2}x+6\), so here slope, \(m=\frac{-1}{2}\) which is incorrect.

We know that the line passes through the origin so our equation should be

\(y=\frac{1}{2}x+c\) and at origin we have (0,0)

so \(0=\frac{1}{2}*0+c => c=0\) i.e y-intercept is 0 (as per your equation y intercept is 6 which is incorrect). If a line passes through origin it will not cut y-axis and hence there will be no intercept.

Hence equation of line will be \(y=\frac{1}{2}x\)

now at (x,1) we will have \(1=\frac{1}{2}x=>x=2\)

and at (10,y) we will have \(y=\frac{1}{2}*10 =>y=5\)

Hence \(x+y=2+5=7\)

There is an alternate method as well using only the formula to find slope. This method is also explained in earlier posts.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8085
Location: United States (CA)
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 20 Feb 2018, 17:14
1
manishuol wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =

(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12


Since the slope m of the line is ½ and the line passes through (x, 1) and the origin (0,0), we use the slope formula m = (y1 - y2)/(x1 - x2) and we have:


(1 - 0)/(x - 0) = 1/2

1/x = 1/2

x = 2

Similarly, using the points (10, y) and the origin, we can create the equation:

(y - 0)/(10 - 0) = 1/2

y/10 = 1/2

y = 5

Thus, x + y = 2 + 5 = 7.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13208
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If  [#permalink]

Show Tags

New post 02 Feb 2019, 21:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If   [#permalink] 02 Feb 2019, 21:05
Display posts from previous: Sort by

In the coordinate plane, points (x, 1) and (10, y) are on line k. If

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





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