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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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MathRevolution
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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] In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter   16 Jun 2016, 20:37
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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=2b
2) a=6

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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] In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter   16 Jun 2016, 20:48
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x/a + y/b = 1

The above equation is the intercept equation of a line, in which 'a' is the x intercept of the line and 'b' is the y intercept of the line.
Therefore to find the X intercept we need to find the value of a.

a) a= 2b

Clearly insufficient. Even if substitute the above into the equation we won't get the value of 'a' unless we have a point through which the line passes.

b) a=6
This is sufficient.

Therefore the X intercept of the line is (6,0)

B is the correct.
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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] In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter   19 Jun 2016, 17:45
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We can modify the original condition and the question. When the question asks about the x-intercept, we need to find the value of x when y=0. Then, if we substitute y=0, from x/a=1, we get x=a. Hence, we all need to know the value of a. Since the condition 2) states a=6, the condition is sufficient. Thus, the correct answer is B.



- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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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] In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter   Updated on: 26 Jun 2016, 03:24
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] In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter   24 Jun 2016, 11:49
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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 =
Show Spoiler
B


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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] In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-inter   15 Feb 2024, 02:45
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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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