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# Does the line pass through the first quadrant? I. the line

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Does the line pass through the first quadrant? I. the line [#permalink]

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10 Jan 2008, 11:27
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Does the line pass through the first quadrant?
I. the line has x-intercept=-1
II. the slope of the line is greater than 1

I went for B until someone mentioned that the slope could be infinitely large and hence a vertical line, so E...is that latter point legitimate as far as the gmat is concerned?
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10 Jan 2008, 11:40

We're trying to find out if a line cuts through the first quadrant (top right).

ALL lines with a positive slope will cross through the first quadrant
SOME lines with a negative slope will cross through the first quadrant

I. the line has x-intercept=-1

Tells us that the line crosses the x axis at (-1,0). Whether it passes through the first quadrant depends on it's slope, which we don't have, so this statement is insufficient.

INSUFFICIENT

II. the slope of the line is greater than 1

Tells us that the line has a positive slope, so it WILL pass through the first quadrant.

SUFFICIENT

A vertical line has an undefined slope because slope = rise/run and a vertical line has a run of 0 (and you can't divide by 0) so the slope is undefined. A horizontal line has a slope of 0. The fact that statement 2 says it has a slope greater than 1 tells us it's not a vertical or horizontal line, and that it does cross the first quadrant at some point.
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10 Jan 2008, 11:52
eschn3am wrote:

We're trying to find out if a line cuts through the first quadrant (top right).

ALL lines with a positive slope will cross through the first quadrant
SOME lines with a negative slope will cross through the first quadrant

I. the line has x-intercept=-1

Tells us that the line crosses the x axis at (-1,0). Whether it passes through the first quadrant depends on it's slope, which we don't have, so this statement is insufficient.

INSUFFICIENT

II. the slope of the line is greater than 1

Tells us that the line has a positive slope, so it WILL pass through the first quadrant.

SUFFICIENT

A vertical line has an undefined slope because slope = rise/run and a vertical line has a run of 0 (and you can't divide by 0) so the slope is undefined. A horizontal line has a slope of 0. The fact that statement 2 says it has a slope greater than 1 tells us it's not a vertical or horizontal line, and that it does cross the first quadrant at some point.

I do not agree with you. The fact that slope of a line is infinity does not mean that the value of the slope does not exit. The slope of the line x=-1 exits and is greater than 1 and it doesn't cross quadrant I. OA should be E.
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10 Jan 2008, 11:57
Quote:
I do not agree with you. The fact that slope of a line is infinity does not mean that the value of the slope does not exit. The slope of the line x=-1 exits and is greater than 1 and it doesn't cross quadrant I. OA should be E.

Quote:
Verdict: vertical lines have NO SLOPE. That is, the concept of slope just doesn't work for vertical lines. The slope doesn't exist!

http://www.purplemath.com/modules/slope.htm

Well I'm afraid the entire math community agrees with me so I'll stick with B.
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10 Jan 2008, 12:11
The answer lies in the plane of math definitions.
http://en.wikipedia.org/wiki/Slope

"The larger the absolute value of a slope, the steeper the line. A horizontal line has slope 0, a 45° rising line has a slope of +1, and a 45° falling line has a slope of -1. A vertical line's slope is undefined."

I think it origins from a more general math definition: Division by zero.
http://en.wikipedia.org/wiki/Division_(mathematics)

Division by zero (i.e. where the divisor is zero) is not defined.
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Director
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10 Jan 2008, 14:16
walker wrote:
The answer lies in the plane of math definitions.
http://en.wikipedia.org/wiki/Slope

"The larger the absolute value of a slope, the steeper the line. A horizontal line has slope 0, a 45° rising line has a slope of +1, and a 45° falling line has a slope of -1. A vertical line's slope is undefined."

I think it origins from a more general math definition: Division by zero.
http://en.wikipedia.org/wiki/Division_(mathematics)

Division by zero (i.e. where the divisor is zero) is not defined.

OG also agree with you guys. What is the source of this question?
Re: DS technical question   [#permalink] 10 Jan 2008, 14:16
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