In the rectangular coordinate system, line k is defined by the equatio

Question

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.

Kudos for a correct  solution .

shreyast · Answer

Both statements alone are sufficient.

We just need to substitute values of x and y to find out value of n.

X intercept is point of intersection of line with x-axis, so x = 8 and y = 0
Y intercept is point of intersection of line with y-axis, so x = 0 and y = -4

GSBae · Answer

Solving for y, our equation becomes  y = \frac{x}{2} + \frac{n}{2} . We are asked to solve for n.  Notice immediately  that any two values for x and y would allow us to solve the problem, as then it becomes one equation with one unknown.

1) (8,0) is a point on the line. Sufficient.

2) (0,-4) is a point on the line. Sufficient.

Answer: D.

If we wanted to take a further look, we could actually plug in these values and test.

1) 0 = 4 + n/2. n = -8.

2) -4 = n/2. n = -8.

Either option is sufficient. Answer: D

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: findn_exp.png

mvictor · Answer

the equation can be rewritten as:
2y=x+n or y=x/2 + n/2
statement 1 tells us that when y is 0, x is 8. by plugging in the numbers, we can find the value of n - sufficient
statement 2 - it gives directly the value of n/2, thus is sufficient.

D.

MathRevolution · Answer

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.

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.

There are 2 variables (m,n) in y=mx+n, but actually, we only need to know n in order to understand the graph, so we only have one variable (n). There are 2 equations given, so there is high chance (D) is our answer.
For condition 1, it passes through (8,0), 8-2*0+n=0, n=-8. This is sufficient.
For condition 2, is passes through (0,-4), and from 0-2(-4)+n=0, n=-8. This is sufficient as well, making the answer (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

loserunderachiever · Answer

QA : D for me , rationale :

1. Given : x - 2y + n = 0 , x intercept 8 , we can try (8,0) and plug this into the given equation we get , n= -8 SUFFICIENT 
2. y intercept -4 , coordinate ( 0,-4) , if we plug this in the main equation x-2y + n = 0 , We get , 0-2(-4) + n = 0 or n = -8 SUFFICIENT

adkikani · Answer

Bunuel   gmatbusters   niks18   mvictor   amanvermagmat

How about this approach?

The equation of the line in question stem in slope-intersect formula (y = mx+ c) 
gives:

y = (x/2) + n/2

Three unknown variables:y, x and n.

St 1: If a line passes through (8,0) we can know values of x as 8 and y as 0, Substituting the 
same will give me value of n. Sufficient.

St 2: Directly value of n in terms of y-intercept is given. Sufficient

Let me know if my above steps are correct to minimize any calculations in the problem.

GMATBusters · Answer

Hi
Your approach is  right .
But converting the line in the standard form  "y =mx+c"  is not necessary.

Simply, to find x intercept, put y =0 and to find y intercept, put x =o.

BrentGMATPrepNow · Answer

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

Fdambro294 · Answer

Equation of Line in slope intercept form:

Y = (1/2)X + (N/2)

Where the slope = (1/2)
And
The Y Intercept = (N/2)

N = ?

S1:
The X-Intercept is given by the negation of the Y-Intercept divided by the slope

Y-intercept = b = (N/2)

Slope = m = (1/2)

X - Intercept = (-) (b / m)

8 = (-)(n / 2) / (1/2)

8 = (-2n) / 2

8 = -n

n = -8

Sufficient

S2:
Y - Intercept = b = (n/2) = -4

n = -8

Sufficient

D

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