It is currently 19 Nov 2017, 11:10

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# At what angle do line y=Kx + B and line y=Bx+K intersect? 1.

Author Message
CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1076 [0], given: 4

Location: New York City
At what angle do line y=Kx + B and line y=Bx+K intersect? 1. [#permalink]

### Show Tags

19 Nov 2007, 08:32
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

At what angle do line y=Kx + B and line y=Bx+K intersect?

1. B+K=1
2. B*K=0

Please walk me thru this problem.

Kudos [?]: 1076 [0], given: 4

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4662 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

### Show Tags

19 Nov 2007, 08:49
C.

angle(kx+b,bx+k)=angle(kx,bx) y=kx+b (k: slope, b: shift)
k,b - characterize slopes of lines.

1. b+k=1
for example, (b,k)=(0,1) ==> angle=45
(b,k)=(1000001,-1000000) ==> angle~0
insuff.

2. b*k=0
for example, (b,k)=(0,1) ==> angle=45
(b,k)=(0,-1000000) ==> angle~90
insuff.

3. b+k=1, b*k=0 ==> (b,k) e {(0,1);(1,0)}
for both cases angle=45
suff.

Kudos [?]: 4662 [0], given: 360

Manager
Joined: 25 Jul 2007
Posts: 107

Kudos [?]: 22 [0], given: 0

### Show Tags

19 Nov 2007, 08:53
Answer is C. Both statements together are sufficient.

Here is a detailed explanation.

Consider statement 1.

B + K =1.

Substituting this equation in the 2 given equations doesn't tell us much.

Statement 1 is insufficient.

Consider statement 2.

B * K =0.
i.e. either b=0 or k=0 or b=0,k=0.

This does not give us specific information about the position of the lines either.

Consider the two statements together.

B + K =1

&

B * K =0.

That means either B = 0 and K = 1

OR

B = 1 and K = 0.

Considering either of the possibilities in the given line equations leaves us with the same two equations.

i.e y = 1 and y = x

y = 1 is a line parallel to the axis at a height of 1.

y=x will have points such as (0,0), (1,1), (2,2),....

Therefore, these two lines can only intersect at one point (1,1).

We now have an isosceles right angled triangle.

i.e. the two lines intersect at an angle of 45 degrees.

Hope this helps.

Kudos [?]: 22 [0], given: 0

CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1076 [0], given: 4

Location: New York City

### Show Tags

20 Nov 2007, 12:54
good job guys.

OA is C.

slope of 1 is 45 deg
slope of 0 is flat, parallel to x axis
intersect at 45 deg.

Kudos [?]: 1076 [0], given: 4

Director
Joined: 11 Jun 2007
Posts: 633

Kudos [?]: 439 [0], given: 0

### Show Tags

20 Nov 2007, 13:36
Another way (more useful for arbitrary angles):
easy formula for any general straight lines:

The angle between two lines y = m1x + c1 and y = m2x + c2 is tan inverse of the modulus of : [(m1 - m2)/(1 + m1*m2)]

tan X = ( B - K)/(1 + B*K)

case 1: tan X = ( B - K)/(1 + B*K) ( not sufficient)

case 2: tan X = (B - K) (not sufficient)

combine case 1 and 2:

tan X = (B - K) where K = 0 or B = 0. Therefore, B = 1 or K = 1 respectively.

Hence tan X = 1;(taking the positive angle) X = 45 degrees.

Kudos [?]: 439 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15655

Kudos [?]: 282 [0], given: 0

Re: At what angle do line y=Kx + B and line y=Bx+K intersect? 1. [#permalink]

### Show Tags

22 Feb 2017, 20:31
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.
_________________

Kudos [?]: 282 [0], given: 0

Re: At what angle do line y=Kx + B and line y=Bx+K intersect? 1.   [#permalink] 22 Feb 2017, 20:31
Display posts from previous: Sort by

# At what angle do line y=Kx + B and line y=Bx+K intersect? 1.

Moderator: chetan2u

 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®.