challenge DS

[Night reader]

In the xy-plane, if line m has negative slope and passes through the point (r; 6), is the x-intercept of line m positive?

(1) The slope of line m is - 1/2

(2) r > 0

[4GMAT_Mumbai]

Hi,

Thanks for the interesting Q ...

1. The x intercept could either be -ve or +ve as it entirely depends on the value of r. If the line meets the x-axis at (a,0);

then the slope = (6-0) / (r - a) = -0.5

12 = a-r.

Whether a is +ve or not depends on r. Hence, insuff ...

2. r > 0.

then slope = (6-0) / (r - a) = some -ve number

So, r - a < 0

a > r

a > a positive r.

So, a also has to be +ve.

Answer: B ?

[Night reader]

Hi,

Thanks for the interesting Q ...

1. The x intercept could either be -ve or +ve as it entirely depends on the value of r. If the line meets the x-axis at (a,0);

then the slope = (6-0) / (r - a) = -0.5

12 = a-r.

Whether a is +ve or not depends on r. Hence, insuff ...

2. r > 0.

then slope = (6-0) / (r - a) = some -ve number

So, r - a < 0

a > r

a > a positive r.

So, a also has to be +ve.

Answer: B ?

flawless reasoning and correct answer! thanks

BTW, when the e-book of 4gmat on number theory and inequalities will be available? I got one for perms, prob and combin. - awesome stuff

[Anurag@Gurome]

In the xy-plane, if line m has negative slope and passes through the point (r; 6), is the x-intercept of line m positive?

(1) The slope of line m is - 1/2
(2) r > 0

Sometimes the problems on coordinate geometry can be easily solved by drawing or visualizing the scenario. This problem is a good example to learn that. See the below figure.


Statement 1: two lines are shown with negative slope (I've not shown the slope as the value of the slope doesn't matter), one of them has positive x-intercept and other one has negative.

Not sufficient

Statement 2: As r is positive, the point (r, 6) lies on the first quadrant. Any line having negative slope and passing through any point on the first quadrant must have a positive x-intercept.

Sufficient.

The correct answer is B.

[ankur.agrawal]

Hi,

Thanks for the interesting Q ...

1. The x intercept could either be -ve or +ve as it entirely depends on the value of r. If the line meets the x-axis at (a,0);

then the slope = (6-0) / (r - a) = -0.5

12 = a-r.

Whether a is +ve or not depends on r. Hence, insuff ...

2. r > 0.

then slope = (6-0) / (r - a) = some -ve number

So, r - a < 0

a > r

a > a positive r.

So, a also has to be +ve.

Answer: B ?

flawless reasoning and correct answer! thanks

BTW, when the e-book of 4gmat on number theory and inequalities will be available? I got one for perms, prob and combin. - awesome stuff

Hi dude. I am facing sum hiccups pn P& C & Probability. Is the E-book of 4GMAT a good buy.

[anshumishra]

In the xy-plane, if line m has negative slope and passes through the point (r; 6), is the x-intercept of line m positive?

(1) The slope of line m is - 1/2
(2) r > 0

Sometimes the problems on coordinate geometry can be easily solved by drawing or visualizing the scenario. This problem is a good example to learn that. See the below figure.


Statement 1: two lines are shown with negative slope (I've not shown the slope as the value of the slope doesn't matter), one of them has positive x-intercept and other one has negative.

Not sufficient

Statement 2: As r is positive, the point (r, 6) lies on the first quadrant. Any line having negative slope and passing through any point on the first quadrant must have a positive x-intercept.

Sufficient.

The correct answer is B.

Nicely done Anurag !
Graphical approach helps a lot. Many a times, it helps us from making silly mistakes.