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by danjuma » Fri Nov 26, 2010 10:53 pm
In the XY-plane , the line K passes through the origin and through the point (a, b), where ab is not equal to zero. Is b positive?

a. The slope of line K is negative

b. a< b

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by selango » Fri Nov 26, 2010 11:07 pm
stmt1,

slope is negative.

So the point (a,b) are in either second quadrant(-a,b) or fourth quadrant(a,-b)

Insuff

stmt2,

a<b

No info abt signs of a and b.

Insuff

combining 1 and 2,

Since a<b the points must be in second quadrant(-a,b).

b is positive,

Suff

Pick C
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by goyalsau » Sat Nov 27, 2010 3:11 am
selango wrote:stmt1,

slope is negative.

So the point (a,b) are in either second quadrant(-a,b) or fourth quadrant(a,-b)
Can you please this a bit further,

I was thinking that line is goes downwards when slope is negative, I did not know that it can not be in I and III Quadrant, Can you please tell why is that so,
Saurabh Goyal
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by selango » Sat Nov 27, 2010 3:21 am
If the slope is negative,the line goes downwards.

So the points can be in second quadrant(-a,b) or fourth quadrant(a,-b).

If the slope is positive,the line goes upwards.

So the points can be in first quadrant(a,b) or third quadrant(-a,-b).
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by goyalsau » Sat Nov 27, 2010 3:49 am
selango wrote:If the slope is negative,the line goes downwards.

So the points can be in second quadrant(-a,b) or fourth quadrant(a,-b).

If the slope is positive,the line goes upwards.

So the points can be in first quadrant(a,b) or third quadrant(-a,-b).

Is that rule is compulsory for any line or only those lines that are passing through the origin ,
Can you please explain why is that so??????????
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by Brent@GMATPrepNow » Tue Jun 11, 2019 7:02 am
danjuma wrote:In the XY-plane , the line K passes through the origin and through the point (a, b), where ab is not equal to zero. Is b positive?

1. The slope of line K is negative
2. a< b
Target question: Is b (the y-coordinate of the point on the line) positive?

Given: Line k passes through the origin and through the point (a,b)

Statement 1: The slope of line k is negative
There are several lines and points that satisfy statement 1. Here are two:

Case a:
Image
In this case, b (y-coordinate) is positive. So, the answer to the target question is YES, b is positive

Case b:
Image
In this case, b (y-coordinate) is negative. So, the answer to the target question is NO, b is NOT positive

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a < b
There are several lines and points that satisfy statement 2. Here are two:

Case a:
Image
In this case, b (y-coordinate) is positive. So, the answer to the target question is YES, b is positive

Case b:
Image
In this case, b (y-coordinate) is negative. So, the answer to the target question is NO, b is NOT positive

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the slope of line k is negative. This means line k passes through quadrants II and IV.
Image
In quadrant II, a (the x-coordinate) is always negative, and b (the y-coordinate) is always positive
In quadrant IV, a (the x-coordinate) is always positive, and b (the y-coordinate) is always negative

Statement 2 tells us that a < b
This means that the point (a,b) must be in quadrant II (because, all points in quadrant IV are such that the x-coordinate (a) is greater than the y-coordinate (b)
If point (a,b) is in quadrant II, we can be certain that b (the y-coordinate) is positive
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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