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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.

If the slope is positive,the line goes upwards.

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by goyalsau » Sat Nov 27, 2010 3:49 am
selango wrote:If the slope is negative,the line goes downwards.

If the slope is positive,the line goes upwards.

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??????????
Saurabh Goyal
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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:

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

Case b:

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:

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

Case b:

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.

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