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# Is the slope of line q negative?

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Manager
Joined: 10 Mar 2014
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Is the slope of line q negative?  [#permalink]

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12 Jan 2015, 08:27
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Difficulty:

25% (medium)

Question Stats:

67% (00:31) correct 33% (00:36) wrong based on 172 sessions

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Is the slope of line q negative?

(1) Line q has a negative x-intercept.
(2) Line q passes through Quadrant I.
Manager
Joined: 13 Sep 2014
Posts: 87
WE: Engineering (Consulting)
Re: Is the slope of line q negative?  [#permalink]

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12 Jan 2015, 09:02
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
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Re: Is the slope of line q negative?  [#permalink]

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12 Jan 2015, 09:25
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.
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Re: Is the slope of line q negative?  [#permalink]

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13 Jan 2015, 00:47
option C

Attachments

Q.JPG [ 16.56 KiB | Viewed 2791 times ]

Senior Manager
Status: Math is psycho-logical
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Re: Is the slope of line q negative?  [#permalink]

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05 Mar 2015, 11:22
DesiGmat wrote:
option C

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...
Attachments

q1.png [ 2.12 KiB | Viewed 2652 times ]

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Re: Is the slope of line q negative?  [#permalink]

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05 Mar 2015, 11:43
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).

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Senior Manager
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Is the slope of line q negative?  [#permalink]

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05 Mar 2015, 11:48
EMPOWERgmatRichC wrote:
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

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!
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Re: Is the slope of line q negative?  [#permalink]

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18 Sep 2016, 07:02
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).
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Is the slope of line q negative?  [#permalink]

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18 Sep 2016, 08:28

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.

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Re: Is the slope of line q negative?  [#permalink]

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26 Nov 2018, 23:28
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Re: Is the slope of line q negative? &nbs [#permalink] 26 Nov 2018, 23:28
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