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by GmatKiss » Sun May 20, 2012 9:22 am
In the rectangular coordinate system, line k is defined by the equation x - 2y + n = 0. What is the value of n?

(1) The x-intercept of line k is 8.

(2) The y-intercept of line k is -4.
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by neelgandham » Sun May 20, 2012 11:11 am
In the rectangular coordinate system, line k is defined by the equation x - 2y + n = 0. What is the value of n?

Let us try to convert it into the intercept form, i.e. (x/a)+(y/b)=1, where a is the x - intercept and b is the y intercept.

x - 2y + n = 0
x - 2y = -n
(x/-n) +(y/(n/2)) = 1. So x-intercept of the line is -n and the y-intercept n/2
(1) The x-intercept of line k is 8.

The x-intercept of line k is 8 = -n. So n = -8.
Statement 1 is sufficient to answer the question.
(2) The y-intercept of line k is -4.
The y-intercept of line k is -4 = n/2. So n = -8.
Statement 2 is sufficient to answer the question.

IMO D
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by Anurag@Gurome » Sun May 20, 2012 9:02 pm
GmatKiss wrote:In the rectangular coordinate system, line k is defined by the equation x - 2y + n = 0. What is the value of n?

(1) The x-intercept of line k is 8.

(2) The y-intercept of line k is -4.
An x-intercept is a point on the graph where y is zero, and a y-intercept is a point on the graph where x is zero. In other words, an x-intercept is a point in the equation where the y-value is zero, and a y-intercept is a point in the equation where the x-value is zero.

x - 2y + n = 0

(1) The x-intercept of line k is 8 implies y = 0 and x = 8. So, 8 + n = 0 or n = -8; SUFFICIENT.

(2) The y-intercept of line k is -4 implies x = 0 y = -4. So, 8 + n = 0 or n = -8; SUFFICIENT.

The correct answer is D.
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Re: coordinate

by Brent@GMATPrepNow » Mon Jan 20, 2020 7:39 am
GmatKiss wrote: ↑
Sun May 20, 2012 9:22 am
 In the rectangular coordinate system, line k is defined by the equation x - 2y + n = 0. What is the value of n?

(1) The x-intercept of line k is 8.

(2) The y-intercept of line k is -4.
KEY CONCEPT: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of the line.

Given: Line k is defined by the equation x - 2y + n = 0

Target question: What is the value of n?

Statement 1: The x-intercept of line k is 8
In other words, the point (8, 0) lies ON the line, which means x = 8 and y = 0 SATISFY the equation x - 2y + n = 0
Plug in values to get: 8 - 2(0) + n = 0
Simplify: 8 + n = 0
Solve: n = -8
So, the answer to the target question is n = -8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The y-intercept of line k is -4
In other words, the point (0, -4) lies ON the line, which means x = 0 and y = -4 SATISFY the equation x - 2y + n = 0
Plug in values to get: 0 - 2(-4) + n = 0
Simplify: 8 + n = 0
Solve: n = -8
So, the answer to the target question is n = -8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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