Data Sufficiency

BTGmoderatorLU wrote:Source: Magoosh

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 \(-4\).

The OA is D

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