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

 It is currently 19 Oct 2019, 15:12 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

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.  A line has a slope of 3/4 and intersects the point (-12, -39). At whic

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

Hide Tags

Current Student B
Joined: 06 Sep 2015
Posts: 21
Location: Brazil
GPA: 3.74
A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

7 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:42) correct 29% (02:04) wrong based on 339 sessions

HideShow timer Statistics

A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis?

A. (40,0)
B. (30,0)
C. (0,40)
D. (40,30)
E. (0,30)

My solutuion was:

y=3/4x+b
-39=3/4(-12)+b
-39=-9+b
b=-30

But he asks for x-axis, I´m confused here...

thanks
Solution by the book: (40,0)

Originally posted by bitenca on 12 Dec 2015, 07:17.
Last edited by ENGRTOMBA2018 on 12 Dec 2015, 07:21, edited 1 time in total.
Formatted the question
CEO  S
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

2
1
bitenca wrote:
A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis?

A. (40,0)
B. (30,0)
C. (0,40)
D. (40,30)
E. (0,30)

My solutuion was:

y=3/4x+b
-39=3/4(-12)+b
-39=-9+b
b=-30

But he asks for x-axis, I´m confused here...

thanks
Solution by the book: (40,0)

I have modified your original post.

As for your question,

Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.

You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.

Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.

After substituting the above values, you get c = -30.

Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.

Put y=0 in the above equation of the line and you will get, x=40.

Thus, the point of intersection is (40,0).

A is the correct answer.
Current Student B
Joined: 06 Sep 2015
Posts: 21
Location: Brazil
GPA: 3.74
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

Engr2012 wrote:
bitenca wrote:
A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis?

A. (40,0)
B. (30,0)
C. (0,40)
D. (40,30)
E. (0,30)

My solutuion was:

y=3/4x+b
-39=3/4(-12)+b
-39=-9+b
b=-30

But he asks for x-axis, I´m confused here...

thanks
Solution by the book: (40,0)

I have modified your original post.

As for your question,

Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.

You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.

Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.

After substituting the above values, you get c = -30.

Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.

Put y=0 in the above equation of the line and you will get, x=40.

Thus, the point of intersection is (40,0).

A is the correct answer.

Ohh.. Now I see, thank you very much!!

Eddie
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

1
bitenca wrote:
A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis?

A. (40,0)
B. (30,0)
C. (0,40)
D. (40,30)
E. (0,30)

My solutuion was:

y=3/4x+b
-39=3/4(-12)+b
-39=-9+b
b=-30

But he asks for x-axis, I´m confused here...

thanks
Solution by the book: (40,0)

One last point to make:

Even if we aren't sure how to actually answer the question, we can still recognize that for any point on the x-axis, the y-coordinate will equal 0.
This one fact allows us to ELIMINATE answer choices C, D and E, leaving us with a 50% chance of guessing the correct answer.

Here's a free video about x- and y-intercepts on the GMAT - http://www.gmatprepnow.com/module/gmat- ... /video/996

Cheers,
Brent
_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

1
1
Hi bitenca,

This question can be solved in a couple of different ways. If you're comfortable with the 'concept' of 'slope', then you can answer this question with just a bit of arithmetic.

We're given some information about a line:
1) The line has a slope of 3/4
2) The line intersects the point (-12,-39)

We're asked at which point the line will intersect the X-axis. Since THAT co-ordinate will be (X, 0), we can use the slope to our advantage and 'count up' to that point:

With a slope of 3/4, we know that the line will "go up 3 points and go forward 4 points", meaning that the first few co-ordinates would be...

(-12,-39)
(-8, -36)
(-4, -33)
(0, -30)
Etc.

We can continue to 'count up' from here OR do a bit of algebra:

From the original co-ordinate, we know that we have to increase the '-39' to a '0' in increments of 3. That will clearly take 13 increments (since 13x3 = 39). Those same 13 increments would 'add 4' each time to the original X co-ordinate, turning '-12' into.....-12 + (13x4) = 40. Thus, the answer is (40,0).

GMAT assassins aren't born, they're made,
Rich
_________________
Senior Manager  B
Joined: 02 Dec 2014
Posts: 354
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications)
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

1
The equation of the slope is (y2-y1)/(x2-x1). Here we have (y2+39)/(x2+12)=(3/4) ==> 4y +156=3x+36 . We need to find x-interscetion i.e the point where y=0 Hence we have 3x=120 and x=40 Point of x-intersection is (40,0) Answer A
_________________
"Are you gangsters?" - "No we are Russians!"
Intern  Joined: 28 Jul 2016
Posts: 10
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

--> Equation of line with slope m and passing through (x1,y1) = (y-y1)=m(x-x1)
So here m=3/4 and (x1,y1)=(-12,-39). So equation of line: (y+39)=3/4(x+12) ==> (y+39)=(3/4x+9)
Now point where this line cuts x-axis is where y=0.
So equation becomes: 0+39=3/4x+9 Therefore, x=40 (when y=0)

Manager  S
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 66
GMAT 1: 750 Q50 V42 WE: Education (Education)
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

Since we are looking for point on x axis, y coordinate should be zero,
Thus we can eliminate option C, D, E
Looking at option A
40,0
slope = $$\frac{change in y}{change in x}$$= $$\frac{y_2-y_1}{x_2-x_1}$$
ie. slope = $$\frac{-39-0}{-12-40}$$=$$\frac{3}{4}$$
thus option A is answer
_________________
Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com
Intern  B
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
GPA: 3.4
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

One can solve these type of questions easily if he/she knows who to convert given points into to slope equation. For example, the author gives two points (x,y) (x1,y1), and requires to turn these into y=mx+k form.
Here is a great post bu Bunuel , check it out! https://gmatclub.com/forum/math-coordin ... ml#p659245
For this particular problem, the author gives us the slope of the equation, as well as one coordinate, such as slope= 3/4 and the coordinate, is (-12,-39).
$$\frac{y-(-39)}{x-(-12)}$$ =$$\frac{3}{4}$$
4(y+39)=3(x+12), so y=3x/4-30. To the the x intercept, we should plug in 0 for the y, and find out the coordinate, (40,0).
_________________
Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

What you think, you become,
What you feel, you attract,
What you imagine, you create.
Non-Human User Joined: 09 Sep 2013
Posts: 13275
Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic  [#permalink]

Show Tags

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.
_________________ Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic   [#permalink] 09 Oct 2019, 08:06
Display posts from previous: Sort by

A line has a slope of 3/4 and intersects the point (-12, -39). At whic

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

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