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In the xy-plane, if a line has a y-intercept greater than 2,

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In the xy-plane, if a line has a y-intercept greater than 2, [#permalink]

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New post 30 Jul 2008, 01:23
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In the xy-plane, if a line has a y-intercept greater than 2, is its x-intercept less than -3?
(1) The line passes through point (-2,2).
(2) The slope of the line is 1/2.
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.

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Re: coordinate geometry [#permalink]

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New post 30 Jul 2008, 02:42
I think the ans is B

here is my reasoning ..

lets say eqn of line is y = mx+c where m - slope and c is y-intercept

now for x-intercept y = 0

so in abv eqn we get ...

0=mx+c
so x-intercpt = -c/m

so if can show that c/m > 3 we done

Stmt 1 (2,-2) is on line

so 2= m(-2) +c

m = (2-c) /(-2)

now coz c>2 given
so we cn rewrite abv as .. m = (c-2)/2

so our req c/m = c /( c-2 /2)

=> 2c/( c-2)

this can be greater than 3 or equal to 3 or even less than 3 depending values of c hence not sufficient

Stmt (2) slope is 1/2

so our req = c/(1/2) = 2c

now as c> 2 so 2c > 4

hence x-intercept will be less than -3

Stmt 2 is suff

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Re: coordinate geometry [#permalink]

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New post 30 Jul 2008, 02:59
yes B should be the answer....

IMO the best way to solve such problems is to draw xy plane ....

st 1 : there can be many lines possible passing from (-2,2) with y intercept > 2 and still have x intercepts more or less t han - 3

St 2 : all lines with slope 1/2 are || lines... seperate out ones with having y intercept moe than 2... you'll clearly see that all these lines will have x intercept less than -4 .... Suff

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Re: coordinate geometry [#permalink]

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New post 30 Jul 2008, 03:29
Good question.

I agree with B.

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Re: coordinate geometry [#permalink]

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New post 30 Jul 2008, 04:02
I got B because we can determine a specific equation.

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Re: coordinate geometry [#permalink]

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New post 03 Aug 2008, 11:06
arjtryarjtry wrote:
In the xy-plane, if a line has a y-intercept greater than 2, is its x-intercept less than -3?
(1) The line passes through point (-2,2).
(2) The slope of the line is 1/2.
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.


y=mx+c => y/c + (x)/(-c/m) =1 => x intercept = -c/m
y intercept= c
c>2 is given
now (-2,2) satisfies eqn y=mx+c => m=(c-2)/2 =>c>2 => m >0 =>
-c/m <0 => when m=1/2 ,c=3 -c/m <-3 and when m=2 ,c=3 -c/m >-3
INSUFFI

(2) m=1/2 and c>2 => -c/m <-4 => -c/m <-3 hence SUFFI

IMO B
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Re: coordinate geometry   [#permalink] 03 Aug 2008, 11:06
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In the xy-plane, if a line has a y-intercept greater than 2,

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