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# In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter

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In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter [#permalink]
MathRevolution wrote:
In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-intercept of line K?
1) a=2b
2) a=6

*An answer will be posted in 2 days.

Given x/a + y/b = 1
=> bx+ay / ab = 1
=> ay + bx = ab
=> ay = -bx + ab
=> y = - (b/a) x + ab

Now the above equation is in the form of y= mx + c where c is y-intercept.

Here we are asked to find the x intercept.

Then consider y = 0
=> 0 = - (b/a) x + ab
=> -ab = - (b/a) x
=> a = x/a
=> $$a^2$$ = x.

In order to know the value of x we need to have the value of a

Stat 1 : a = 2b , insufficient as we don't know the value of a or b.

Stat 2 : a= 6 , then x = 36. Sufficient.

Thus correct answer is B.

Originally posted by msk0657 on 23 Jun 2016, 22:28.
Last edited by msk0657 on 26 Jun 2016, 03:24, edited 1 time in total.
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In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter [#permalink]
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MathRevolution wrote:
In the x-y plane there is a line K, (x/a) + (y/b)=1. What is the x-intercept of line K?

1) a = 2b
2) a = 6

Target question: What is the x-intercept of line K?

This is a great candidate for rephrasing the target question.

Given: the equation of line K is (x/a) + (y/b) = 1.
NOTE: The x-intercept is the x-coordinate of the point where the line intersects the x-axis
IMPORTANT: At this intersection point, the y-coordinate = 0
So, let's plug y = 0 into the equation of line K
We get: (x/a) + (0/b) = 1
Simplify: (x/a) = 1
This means that x = a
In other words, the x-intercept of like K is a
So, we need only find the value of a to answer the target question.

Let's REPHRASE the target question as.....
REPHRASED target question: What is the value of a?

Statement 1: a = 2b
This is not enough info to answer the REPHRASED target question. There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 4 and b = 2, in which case a = 4
Case b: a = 6 and b = 3, in which case a = 6
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a = 6
PERFECT!!
This allows us to answer the REPHRASED target question with certainty. So statement 2 is SUFFICIENT

Answer =

RELATED VIDEO
Here's a video with tips on rephrasing the target question:

Cheers,
Brent
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Re: In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter [#permalink]
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Re: In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter [#permalink]
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