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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]

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New post 20 Mar 2017, 02:41
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A
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Question Stats:

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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=b
2) a=1

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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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New post 20 Mar 2017, 04:18
for a line k: (x/a)+(y/b)=1, x- intercept will be a

to find exact value. we need the value of a

St 1: a=b. no fixed value can be interpreted. INSUFFICIENT
St 2: a = 1. ANSWER

Option B
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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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New post 20 Mar 2017, 06:53
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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 = b
2) a = 1


Target question: What is the x-intercept of line K?
This is a great candidate for rephrasing the target question.

Given: (x/a) + (y/b) = 1
The x-intercept is the value of x that satisfies the equation when y = 0
So, plug y = 0 into the equation to get: (x/a) + (0/b) = 1
Simplify: x/a = 1
So, x = a
In other words, given the equation (x/a) + (y/b) = 1, the x-intercept will be a
REPHRASED target question: What is the value of a?

----now onto the question!!------------

Statement 1: a = b
Since we don't know the value of b, we can't determine the value of a
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a = 1
PERFECT!
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

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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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New post 20 Mar 2017, 08:03
If we need x intercept then y should be equal to 0 in the given equation.

So the given equation becomes X=a.

1. a= b
then X=a = b ( no unique solution )
Not Sufficient
2. a=1
then X=a=1 ( Unique Solution)
Sufficient

So Ans : B Only Statement 2 is sufficient to answer the given question.

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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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New post 22 Mar 2017, 01:48
==> If you modify the original condition and the question, the x-intercept is the value of x when y=0, hence from (x/a)=1, you get x=a, so you only need to find a.

Therefore, the answer is B.
Answer: B
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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 &nbs [#permalink] 21 Sep 2018, 22:32
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