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

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Manager
Joined: 10 Oct 2008
Posts: 56
In the xy-plane, the line k passes through the origin and [#permalink]

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10 Oct 2008, 11:53
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In the xy-plane, the line k passes through the origin and through the point (a, b), where ab ≠ 0. Is b positive?
(1) The slope of line k is negative.
(2) a < b

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Senior Manager
Joined: 21 Apr 2008
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Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
Re: x, y plane [#permalink]

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13 Oct 2008, 10:15
are not there answers?

OA is C but I don't understand why

Cheers
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Intern
Joined: 30 Sep 2008
Posts: 10
Re: x, y plane [#permalink]

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13 Oct 2008, 10:56
1
KUDOS
statement 1
slope is negative. Therefore slop is like \. If slope is like that it passes through the (-x,+y) quadrants and (+x,-y) quadrants. therefore b (or y in this case) could be positive or negative.

statement 2
a < b. this is the same is x< y. This could be anywhere on a graph. eg (-3,-2), (2,3). so b (or y) could be positive or negative.

Both together. If slope is \ (pass through (-x,+y) and (+x,-y) quadrants) and a < b, therefore it is in quadrant (-x,+y). THerefore, b (in this case y) is positive.

Ans is C.

Don't stress, I would have gotten it wrong too, if you didn't put the answer.
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Joined: 21 Apr 2008
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Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
Re: x, y plane [#permalink]

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13 Oct 2008, 11:08
Thank you Piper!

From your explanation I realized that I missed the part that the line crosses the origin. Therefore, there are just two possibilities, as you said.

Cheers
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SVP
Joined: 17 Jun 2008
Posts: 1507
Re: x, y plane [#permalink]

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13 Oct 2008, 12:34
C.

In the attached diagram, x intercept (a) will be smaller to y intercept (b) only if b is positive.
Attachments

untitled.JPG [ 8.23 KiB | Viewed 1512 times ]

Senior Manager
Joined: 04 Aug 2008
Posts: 370
Re: x, y plane [#permalink]

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18 Oct 2008, 13:21
scthakur wrote:
C.

In the attached diagram, x intercept (a) will be smaller to y intercept (b) only if b is positive.

Can someone clarify this problem again.... i got stuck

OA is C but I get E

What if the point (a,b) lies on (-2,-1)

slope is negative as in the graph

the problem says that line goes thru the origin - what is the origin?
line can travel thru 3 quadrants
-x,y -x,-y and x,-y
or
-x,y x,y and x,-y

and -2 < -1 so a<b

both conds satsified
still, b is negative?

Therefore E

because

point a can be (-1,2) and b is positive
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VP
Joined: 17 Jun 2008
Posts: 1329
Re: x, y plane [#permalink]

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19 Oct 2008, 00:29
I got E initially since i overlooked the infio saying this line passes thro origin
now lets take a line y=mx which passes thro origin

acc to given condition : b=am
hence 1)when m<0 b=am but a ca be +ve or -ve hence b can vary INSUFFI

2)now it says b>a => m can be any sign hence can say whether b>0 or<0

Combine both b=ma m<0 and b>a =>b>0
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VP
Joined: 30 Jun 2008
Posts: 1022
Re: x, y plane [#permalink]

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19 Oct 2008, 00:36
Jcpenny wrote:
In the xy-plane, the line k passes through the origin and through the point (a, b), where ab ≠ 0. Is b positive?
(1) The slope of line k is negative.
(2) a < b

line k passes through (0,0) and (a,b). using this we can find slope = (b-0)/(a-0) = b/a

(1) (b/a) < 0 . This means either b or a is negative. But we are not sure which one.

(2) b > a . Not sufficient obviously

(1) and (2) ==> either b or a is negative. if b>a then b has to be positive and a has to be nagative.

Hence C
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Re: x, y plane   [#permalink] 19 Oct 2008, 00:36
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# In the xy-plane, the line k passes through the origin and

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