Is the slope of line q negative?

Question

(1) Line q has a negative x-intercept.
(2) Line q passes through Quadrant I.

sanket1991 · Answer

Slope of the line is nothing but Tan of the angle it makes with x axis (right side)

Clearly both statement alone are not sufficient

Both together Line has to make an acute angle with x axis --> tan of that angle has to be positive and slope too. 
So slope of line q is positive (not negative) hence ans, C

aeropower · Answer

For this question, I would visualize it.

1) - negative x intercept, you could have either a positive or negative slope right? - Insufficient
2) - passes through quadrant 1, again you could have a line that is either positive or negative slope right? - Insufficient

Test together - if you choose a line that must have a negative x intercept, let's choose -5. If the slope is positive, it will pass through Quandrant 1, if the slope is negative, it cannot pass through 1 as it goes through quadrant 4. Since 2 tells you it passes through quandrant 1 - you know the slope must be positive.

So the answer is NO, the slope is positive - C, you'll need both statements.

DesiGmat · Answer

option C

Please find attached the figure.

pacifist85 · Answer

Hi, I thought I understood this question until I saw this image. Is the line in the last (combined) coordinate plane correct?

The y intercept is where the line crosses the y axis, right? If yes, then the line should cross the bottom part of y (the horizontal axis) at some point.

Then, if the line in the plane has to go through Q 1, it should look like in the following graph, or am I wrong? Otherwise, it is not crossing the y axis...

EMPOWERgmatRichC · Answer

Hi pacifist85,

In the original prompt, Fact 1 tells us that the X-INTERCEPT of Line L is negative. In your drawing, you've made the X-intercept POSITIVE (so the drawing does not match the Facts and is incorrect).

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

pacifist85 · Answer

Oh I am sorry... Did I read y intercept instead of x intercept? Probably... Or perhaps I dragged the question into the answer choices trying to make the intercept negative and mixing everything up. Whatever I did, my bad!

Nevernevergiveup · Answer

Original Solution: C

Explanation by Veritas prep:

If a line has a negative x-intercept, that means that its slope and its y-intercept must share a sign: either both are negative or both are positive. (Remember that the x-intercept can be expressed as –(b/m), so if only one of those values is negative, then –(b/m) must be positive, making a positive x-intercept.) Statement (1) is thus INSUFFICIENT. Statement (2) is useless: any line can pass through Quadrant 1; INSUFFICIENT. Combine the statements and visualize the line. If the line crosses the x-axis to the left of zero, then it can only go through Quadrant I if it has a positive slope; if it had a negative slope, it would pass through Quadrants II, III, and IV. (C).

Nevernevergiveup · Answer

Is the slope of line q negative?

since we have intercepts, slopes and quadrants in picture, let me take the equation of line as   \frac{x}{a}+\frac{y}{b}=1   or   y=-(\frac{b}{a})x+b   where slope of the line is   -(\frac{b}{a})

statement 1: Line q has a negative x-intercept.

a  is negative say  -1  (any negative integer)
by substituting  a=-1  we get the equation of line as  y=bx+b 
but still we have no idea what is the sign of b i.e., y intercept can be either positive or negative.
if b is positive slope of line q is positive
if b is negative slope of line q is negative

thus statement 1 is insufficient.

statement 2: Line q passes through Quadrant I. 
 we can easily conclude that line slope can be both positive and negative.
b is positive whereas a can be negative or positive.

Now combine both statements I and II

we know that b is positive in Quadrant I and a is negative.

thus slope is always positive and never negative.

answer  NO  sufficient  YES

mangamma · Answer

Solution: C

If a line has a negative x-intercept, that means that its slope and its y-intercept must share a sign: either both are negative or both are positive. (Remember that the x-intercept can be expressed as –(b/m), so if only one of those values is negative, then –(b/m) must be positive, making a positive x-intercept.) Statement (1) is thus INSUFFICIENT. 
Statement (2) is useless: any line can pass through Quadrant 1; INSUFFICIENT. Combine the statements and visualize the line. If the line crosses the x-axis to the left of zero, then it can only go through Quadrant I if it has a positive slope; if it had a negative slope, it would pass through Quadrants II, III, and IV. (C).

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is the slope of line q negative?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is the slope of line q negative?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards