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

It is currently 18 Jul 2018, 09:03

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

If lines y=mx+b and x=y+bm intersect at a degrees angle

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

Hide Tags

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1264
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post Updated on: 16 Nov 2012, 05:26
7
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:17) correct 40% (01:25) wrong based on 246 sessions

HideShow timer Statistics

If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree

_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com


Originally posted by Marcab on 16 Nov 2012, 03:45.
Last edited by Bunuel on 16 Nov 2012, 05:26, edited 1 time in total.
Renamed the topic.
Jamboree Discount CodesVeritas Prep GMAT Discount CodesOptimus Prep Discount Codes
Most Helpful Community Reply
5 KUDOS received
VP
VP
User avatar
Joined: 02 Jul 2012
Posts: 1192
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: If lines y=mx+b [#permalink]

Show Tags

New post 16 Nov 2012, 03:59
5
1
Marcab wrote:
If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree


To find the angle between two lines, we need to know the slope of both lines. But as shown in the figure, this angle "a" can be either "x" or "y". But since we are given that a<90, we can find out which angle is required because x + y = 180. The slope of the second line is obviously 1. So the question is basically asking for the value of m.

1) Sufficient

2) We get y = bx + b. b is still unknown. Insufficient.

Answer is hence A.

Kudos Please... If my post helped.
Attachments

untitled.JPG
untitled.JPG [ 3.39 KiB | Viewed 6780 times ]


_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

General Discussion
Director
Director
avatar
Joined: 21 Dec 2009
Posts: 554
Concentration: Entrepreneurship, Finance
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 23 Nov 2012, 06:12
Marcab wrote:
If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree

We can find the angle of intersection b/w any 2 lines if we knw the values of their individual slopes.

For y = x + bm, slope is 1; for y = mx + b, slope is "m"
(1) Tan (a) = (m - 1)/(1 + 1*m); tan(a) < 90 if its value is +ve;since m-1>0, no need to add/subtract from 180.
Since statement 2 gives m=2, it is sufficient.
(2) Test y=x+1, y=2x+2 and y=3x+3 with "y=x - 1, y=x-4, and y=x-9"
y=x+1 and y=x gives 0 degrees
y=2x+2 and y=x-4 gives a diffrent value...INSUFF
_________________

KUDOS me if you feel my contribution has helped you.

Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 480
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 15 Feb 2013, 02:51
Folks,
I understand A is sufficient to find the angle.. but how do you find the angle?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

1 KUDOS received
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1264
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 15 Feb 2013, 03:21
1
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 480
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 15 Feb 2013, 03:58
Marcab wrote:
m= tan x.
So x= tan inverse(m).


but m is slope of which line out of the that intersect? :shock:
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Manager
Manager
User avatar
Joined: 24 Sep 2012
Posts: 85
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 20 Feb 2013, 16:07
m is the slope of the line
y=mx+b

If you draw an equation for this line, you will find m to be the slope of the line and b to be the intersect on y axis(when x=0). This is called the slope-intercept form of line equation and you memorizing it will help you deal with such questions. The form of such lines is
y=(slope)x+y-intersect

The other line x=y+bm can be written in a similar fashion

y=x-bm.

Going by the above stated formula, since the coefficient of x=1, slope =1. The y-intersect of the line is bm.

Hope that clarifies your doubt.


Sachin9 wrote:
Marcab wrote:
m= tan x.
So x= tan inverse(m).


but m is slope of which line out of the that intersect? :shock:
2 KUDOS received
Manager
Manager
avatar
Joined: 31 Dec 2012
Posts: 69
Location: India
Concentration: Strategy, Operations
GMAT 1: 700 Q50 V33
GPA: 3.6
WE: Information Technology (Consulting)
Reviews Badge
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 05 Mar 2013, 18:25
2
Angle between 2 lines is m1-m2/1+m1m2 ..

We already know slope of line X = Y + bm.

Option A tells slope of line A - so suffcient but option B tells nothing so not sufficient
Director
Director
User avatar
P
Joined: 27 May 2012
Posts: 504
Premium Member
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 01 Aug 2013, 00:34
abhisingla wrote:
Angle between 2 lines is m1-m2/1+m1m2 ..

We already know slope of line X = Y + bm.

Option A tells slope of line A - so suffcient but option B tells nothing so not sufficient


How do we apply this formula?
In this question m1= 2 and m2=1, does that mean angle is \(\frac{2-1}{1+2.1} = \frac{1}{3}\)
is there a \(tan^{-1}\)before this, so angle between two lines having slopes m1 and m2 \(= tan^{-1}\frac{m1-m2}{1+m1m2}\)

In short how do we actually determine the angle between 2 lines given their slopes?
Thanks
_________________

- Stne

3 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1098
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 01 Aug 2013, 00:48
3
2
stne wrote:
abhisingla wrote:

How do we apply this formula?
In this question m1= 2 and m2=1, does that mean angle is \(\frac{2-1}{1+2.1} = \frac{1}{3}\)
is there a \(tan^{-1}\)before this, so angle between two lines having slopes m1 and m2 \(= tan^{-1}\frac{m1-m2}{1+m1m2}\)

In short how do we actually determine the angle between 2 lines given their slopes?
Thanks


We do not care about the actual measure of the angle.

When we have to determine the angle at which two lines intercept, the ONLY thing we have to know is the slope of each line .
With statement 1 we get (note that I consider only the slopes of the two equations):
line1: \(y=2x\)
line2: \(y=x\)

Once we have those, we are able to determine the length of the angles at the point of intersection. Those angles are fixed and do not change, hence we can determine their length, but in this DS we do not care about the actual number.
With statement 1, can you answer the question? YES, that's enough.

To determine the angle we would have to use formulas that are beyond the scope of the GMAT ("tan" for example) http://planetmath.org/anglebetweentwolines
but the point here, as I said above, is not to find the measure.
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Director
Director
User avatar
P
Joined: 27 May 2012
Posts: 504
Premium Member
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 01 Aug 2013, 01:04
Zarrolou wrote:
stne wrote:
abhisingla wrote:

How do we apply this formula?
In this question m1= 2 and m2=1, does that mean angle is \(\frac{2-1}{1+2.1} = \frac{1}{3}\)
is there a \(tan^{-1}\)before this, so angle between two lines having slopes m1 and m2 \(= tan^{-1}\frac{m1-m2}{1+m1m2}\)

In short how do we actually determine the angle between 2 lines given their slopes?
Thanks


We do not care about the actual measure of the angle.

When we have to determine the angle at which two lines intercept, the ONLY thing we have to know is the slope of each line .
With statement 1 we get (note that I consider only the slopes of the two equations):
line1: \(y=2x\)
line2: \(y=x\)

Once we have those, we are able to determine the length of the angles at the point of intersection. Those angles are fixed and do not change, hence we can determine their length, but in this DS we do not care about the actual number.
With statement 1, can you answer the question? YES, that's enough.

To determine the angle we would have to use formulas that are beyond the scope of the GMAT ("tan" for example) http://planetmath.org/anglebetweentwolines
but the point here, as I said above, is not to find the measure.


That definitely helps ! Other solutions involving tan kept me wondering if indeed it was beyond scope or not,+1
_________________

- Stne

Intern
Intern
avatar
Joined: 04 Jul 2013
Posts: 17
Location: India
Concentration: Operations, Technology
WE: Operations (Manufacturing)
GMAT ToolKit User
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 01 Aug 2013, 01:30
Marcab wrote:
If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree





Correct answer is A

Since Slope of y=mx+b is m let it be m1
and slope of y=x-mb is 1 , let it m2

Now
tan(a) = m1-m2/(1+m1*m2)

ie tan(a) = m-1/(1+m*1)= m-1/m+1


Hence knowing the value m will give us answer
Intern
Intern
avatar
Joined: 05 May 2014
Posts: 4
if lines y = mx + b and y = x + bm [#permalink]

Show Tags

New post Updated on: 17 Jun 2014, 00:22
if lines y = mx + b and y = x + bm intersect at A degrees (A<90) what is the value of angle A

1) m = 2
2) m = b
This is a DS question

The Question has been discussed before: if-lines-y-mx-b-and-x-y-bm-intersect-at-a-degrees-angle-142552.html#p1144329

Originally posted by akshaybansal991 on 17 Jun 2014, 00:02.
Last edited by WoundedTiger on 17 Jun 2014, 00:22, edited 2 times in total.
Topic not mentioned correctly
1 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 701
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: if lines y = mx + b and y = x + bm [#permalink]

Show Tags

New post 17 Jun 2014, 00:21
1
1
akshaybansal991 wrote:
if lines y = mx + b and y = x + bm intersect at A degrees (A<90) what is the value of angle A

1) m = 2
2) m = b
This is a DS question


Hello akshaybansal1991,

Welcome to GC!!

You may want refer to below posts for easier navigation on the site and get more out of Gmatclub

new-to-the-gmat-club-start-here-130870.html
rules-for-posting-in-verbal-gmat-forum-134642.html#p1097623
rules-for-posting-please-read-this-before-posting-133935.html#p1092822

The Question has been discussed before: if-lines-y-mx-b-and-x-y-bm-intersect-at-a-degrees-angle-142552.html#p1144329

Coming back to the question
if lines y = mx + b and y = x + bm intersect at A degrees (A<90) what is the value of angle A

1) m = 2
2) m = b

We know the slope of lines as 1 and m and thus we need to find only m and we can find the angle between 2 lines.

St1 gives you that data and is sufficient
St2 gives you nothing about value of m and hence not sufficient.

Similar question practice
lines-intersecting-angles-m08q15-66826.html#p1235093
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Manager
Manager
avatar
Joined: 28 Apr 2014
Posts: 244
GMAT ToolKit User
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 18 Jun 2014, 07:19
Zarrolou wrote:
stne wrote:
abhisingla wrote:

How do we apply this formula?
In this question m1= 2 and m2=1, does that mean angle is \(\frac{2-1}{1+2.1} = \frac{1}{3}\)
is there a \(tan^{-1}\)before this, so angle between two lines having slopes m1 and m2 \(= tan^{-1}\frac{m1-m2}{1+m1m2}\)

In short how do we actually determine the angle between 2 lines given their slopes?
Thanks


We do not care about the actual measure of the angle.

When we have to determine the angle at which two lines intercept, the ONLY thing we have to know is the slope of each line .
With statement 1 we get (note that I consider only the slopes of the two equations):
line1: \(y=2x\)
line2: \(y=x\)

Once we have those, we are able to determine the length of the angles at the point of intersection. Those angles are fixed and do not change, hence we can determine their length, but in this DS we do not care about the actual number.
With statement 1, can you answer the question? YES, that's enough.

To determine the angle we would have to use formulas that are beyond the scope of the GMAT ("tan" for example) http://planetmath.org/anglebetweentwolines
but the point here, as I said above, is not to find the measure.


Agree that Tan and other trignometry concepts are out of the remit of GMAT but is the formula for angle between two lines m1-m2/1+m1m2 in scope ? In other words can this question come in PS section ?
Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 610
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 10 Aug 2017, 01:55
Marcab wrote:
If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree


Given : 2 lines y = mx+b and y = x-bm. THey interesect at an angle a. Also a < 90
DS : Value of angle a.

a<90, so we know that we need to find only acute angle between the two lines.

Statement 1 : m =2, y = 2x +b, y = x - 2b

So we know the slopes of the two lines and hence the angle between them can be easily found out by the slope fomula
angle a = \(tan^-1 \frac{{m1-m2}}{{1+m1*m2}}\)
SUFFICIENT

Statement 2: m = b, y = bx +b , y = x- b^2

Here the slopes are b and 1 respectively for the two given lines. So we can't find the slope between the two lines.
NOT SUFFICIENT

Answer A
_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Expert Post
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11984
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

Show Tags

New post 25 Jun 2018, 20:30
Hi All,

We're told that the lines Y = (M)(X) + B and X = Y+ (B)(M) intersect at A degrees angle (where A <90 ). We're asked for the value of angle A. To start, this is a complicated-looking graphing question, but ass a category, you're likely to see just 1-2 graphing questions on Test Day and they're normally not this complex.

Since the question asks for the measure of angle A (the smaller angle that forms when the two lines intersect), I would make sure that the lines were in slope-intercept format:

Y = (M)(X) + B
Y = X - (M)(B)

Since we're interested in the angle that forms, we need to focus on the SLOPE of the two lines (the Y-intercept would only determine where each line crosses the Y-axis).

1) M = 2

Based on the information in Fact 1, the lines would be....

Y = 2X + B
Y = X - 2B

No matter what values you choose for B (and then for X and Y), the two lines would have consistent slopes (so they'd always be at the same respective angles, just on different parts of the graph). Try drawing some example pictures and you'll see). This means that the lines will intersect in the exact same way every time and that angle A will always be the same.
Fact 1 is SUFFICIENT.

2) M = B

Since M = B, they could both be 2, 3, 4, 5, etc.

This changes the slope of the first line (depending on the slope), while the slope of the second line stays the same. So, the angle between the two lines would change. If you draw two example pictures, then you see that angle A changes.
Fact 2 is INSUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If lines y=mx+b and x=y+bm intersect at a degrees angle   [#permalink] 25 Jun 2018, 20:30
Display posts from previous: Sort by

If lines y=mx+b and x=y+bm intersect at a degrees angle

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

Events & Promotions

PREV
NEXT


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®.