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# M12#13

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Manager
Joined: 22 Jul 2009
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04 Oct 2009, 13:48
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What is the equation of the line that is perpendicular to line $$y = 2x$$ and passes through point $$(a, b)$$ ?

1. $$a = -b$$
2. $$a - b = 1$$

(C) 2008 GMAT Club - m12#13

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. It is not possible to construct the equation of the line.

Statement (2) by itself is insufficient. It is not possible to construct the equation of the line

Statements (1) and (2) combined are sufficient. They provide a system of linear equations from which $$a = \frac{1}{2}$$ , $$b = -\frac{1}{2}$$ . This is enough to build the equation of the line.

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

For me the answer is D. The perpendicular to $$y = 2x$$ is $$y = -1/2x$$

There is no need for the statements to find the perpendicular. The statements are only good for finding values for a and b. For example, statement 1 gives a=b=0.

Could somebody point out what is wrong with my reasoning?

Thanks

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04 Oct 2009, 20:04
2
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there are infinitely many lines perpendicular to y = 2x, they all have the form

y = (-1/2)x + K

you need to find K to have the complete equation of the line, and to find K, you need to know a point the line passes through.

So far, you only know b = (-1/2)a + K

Statement 1: it tells you (1/2)b = K. not enough
Statement 2: it tells you b = (-1/2)(1+b) + K. not enough.

Together: (1/2)b = K and b = (-1/2)(1+b) + K tell you that a = 1/2, b = -1/2, and K = -1/4
Manager
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04 Oct 2009, 21:16
Thanks Cristofer, that was very helpful. +1
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01 Feb 2011, 05:53
cristofer wrote:
there are infinitely many lines perpendicular to y = 2x, they all have the form

y = (-1/2)x + K

you need to find K to have the complete equation of the line, and to find K, you need to know a point the line passes through.

So far, you only know b = (-1/2)a + K

Statement 1: it tells you (1/2)b = K. not enough
Statement 2: it tells you b = (-1/2)(1+b) + K. not enough.

Together: (1/2)b = K and b = (-1/2)(1+b) + K tell you that a = 1/2, b = -1/2, and K = -1/4

i just wonder at x=o y=k Why cant we substitute k=b? can anyone explain PLZ ?
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01 Feb 2011, 14:15
tinki wrote:
cristofer wrote:
there are infinitely many lines perpendicular to y = 2x, they all have the form

y = (-1/2)x + K

you need to find K to have the complete equation of the line, and to find K, you need to know a point the line passes through.

So far, you only know b = (-1/2)a + K

Statement 1: it tells you (1/2)b = K. not enough
Statement 2: it tells you b = (-1/2)(1+b) + K. not enough.

Together: (1/2)b = K and b = (-1/2)(1+b) + K tell you that a = 1/2, b = -1/2, and K = -1/4

i just wonder at x=o y=k Why cant we substitute k=b? can anyone explain PLZ ?

You could look at the problem this way:

We have a coordinate $$(a,b)$$

1.$$a=-b$$
2.$$a-b=1$$

1) $$a=-b$$ => $$a-b=0$$, there are infinite solutions to the problem a-b=0 and the same goes with 2)

Together:
$$a+b=0$$
$$a-b=1$$
=>
$$2a = 1$$
$$a = 1/2$$
$$b = -1/2$$

We have the coordinate (1/2,-1/2) and now we can solve for the intercept in y=ax+k
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Manager
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02 Feb 2011, 02:17
Mackieman wrote:
tinki wrote:
cristofer wrote:
there are infinitely many lines perpendicular to y = 2x, they all have the form

y = (-1/2)x + K

you need to find K to have the complete equation of the line, and to find K, you need to know a point the line passes through.

So far, you only know b = (-1/2)a + K

Statement 1: it tells you (1/2)b = K. not enough
Statement 2: it tells you b = (-1/2)(1+b) + K. not enough.

Together: (1/2)b = K and b = (-1/2)(1+b) + K tell you that a = 1/2, b = -1/2, and K = -1/4

i just wonder at x=o y=k Why cant we substitute k=b? can anyone explain PLZ ?

You could look at the problem this way:

We have a coordinate $$(a,b)$$

1.$$a=-b$$
2.$$a-b=1$$

1) $$a=-b$$ => $$a-b=0$$, there are infinite solutions to the problem a-b=0 and the same goes with 2)

Together:
$$a+b=0$$
$$a-b=1$$
=>
$$2a = 1$$
$$a = 1/2$$
$$b = -1/2$$

We have the coordinate (1/2,-1/2) and now we can solve for the intercept in y=ax+k

thanks. its all clear . yet i have Doubts why k cant equal to b. any suggestions about that?
will appreciate
Re: M12#13   [#permalink] 02 Feb 2011, 02:17
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# M12#13

Moderator: Bunuel

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