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

## DS

##### This topic has expert replies

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

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

--Anand--

Can you please this a bit further,selango wrote:stmt1,

slope is negative.

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

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

talk_to_saurabh@yahoo.com

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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).

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).

--Anand--

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??????????

Saurabh Goyal

talk_to_saurabh@yahoo.com

-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

talk_to_saurabh@yahoo.com

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EveryBody Wants to Win But Nobody wants to prepare for Win.

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**15003**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1265 members**GMAT Score:**770

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

Answer: C

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

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