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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

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.

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

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

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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?

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

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

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01 Aug 2013, 00:48

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

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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 ?

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

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20 Aug 2015, 19:59

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

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28 Apr 2017, 22:40

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

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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

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