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# In the xy plane, the line k passes through the origin and

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Senior Manager
Joined: 20 Feb 2008
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Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
In the xy plane, the line k passes through the origin and [#permalink]

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01 Dec 2008, 10:44
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In the xy plane, the line k passes through the origin and through points (a,b), where ab NOT EQUAL to 0. Is b positive?

1. The slope of line K is negative
2. a<b
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Joined: 17 Jun 2008
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01 Dec 2008, 10:54

From stmt1 it is clear that the line passes through quadrants 2 and 4. However, point (a,b) can be in either of the quadrants.

Combining stmt2: it is clear that point (a,b) is in the second quadrant.
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Joined: 30 Apr 2008
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01 Dec 2008, 11:06
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KUDOS
Remember that whne we are asked a yes/no question, we need to be able to answer ALWAYS YES or ALWAYS NO. If we ever come up with "sometimes yes" for a statement, then that statement is insufficient.

Statement 1
If the slope is negative, then that means the line will pass through Quandrants II and IV. If a is negative and b is positive, then point (a,b) will be in quadrant II. If a is positive and b is negative ,then the point will be in Quadrant IV. It is good to note that the only way to have a negative slope is when one number is negative and the other is not, otherwise, that point would be on a line with a positive slope.

Which Quadrant doesn't really matter, but it helps you get a mental picture of what's going on with this problem.

Statement 1 is insufficeint because a could be negative, and the point would be in Quadrant II with a positive value for b, or a could be positive and b negative with the point being in Quadrant IV. In this situation, we've satisfied the rule given in statement 1, a negative slope, but cannot answer with an ALWAYS.

Statement 2

If a is less than b. Be careful not to keep thinking of a negative slope with Statement 2. That information came from Statement 1 and is no longer applicable because were considering ONLY Statement 2. Can we ever have a situation where B is positive and a is less than b and also have a situation where B is negative and A is less than B? yes.

{a, b} = {1,2}
{a, b} = {-3, -2}

We have satisfied the rule of a < b and have multiple situations where this rule is followed and b could be either positive or negative. Because we cannot answer ALWAYS positive, Statement 2 is insufficient.

Together
Can we find a situation where both rules presented in the statements are followed? If so, will this result in ALWAYS b = positive or will there still be a SOMETIMES?

Together, the statements are sufficient.

If we MUST have a negative slope, this means that one point, either a or b, must be negative. If b must always be larger than a, it must be the positive value. We cannot have b as a negative value and then a as a smaller negative value because this would mean we have a positive slope and that would vioalte Statement 1. We cannot have b as a positive number, say 5, and then a as a smaller, but still positive number, say 3, because that too would be a positive slope and not conform to Statement 1. So the answer should be C.

ventivish wrote:
In the xy plane, the line k passes through the origin and through points (a,b), where ab NOT EQUAL to 0. Is b positive?

1. The slope of line K is negative
2. a<b

_________________

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a\$\$.

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Senior Manager
Joined: 20 Feb 2008
Posts: 292
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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01 Dec 2008, 11:24
Excellent Reply . Thank you so much for answering my question in such detail

That is the OA.
Re: GMAT PREP   [#permalink] 01 Dec 2008, 11:24
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# In the xy plane, the line k passes through the origin and

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