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If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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12 00:00

Difficulty:   65% (hard)

Question Stats: 55% (02:02) correct 45% (02:19) wrong based on 174 sessions

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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

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Originally posted by Marcab on 16 Nov 2012, 02:45.
Last edited by Bunuel on 16 Nov 2012, 04:26, edited 1 time in total.
Renamed the topic.
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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.

Kudos Please... If my post helped.
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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Folks,
I understand A is sufficient to find the angle.. but how do you find the angle?
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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1
m= tan x.
So x= tan inverse(m).
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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

but m is slope of which line out of the that intersect? _________________
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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.

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

but m is slope of which line out of the that intersect? Manager  Joined: 31 Dec 2012
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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.
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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

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
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if lines y = mx + b and y = x + bm  [#permalink]

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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 16 Jun 2014, 23:02.
Last edited by WoundedTiger on 16 Jun 2014, 23:22, edited 2 times in total.
Topic not mentioned correctly
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Re: if lines y = mx + b and y = x + bm  [#permalink]

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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

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
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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 ?
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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

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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle  [#permalink]

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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.

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