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

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In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 30 Mar 2015, 05:42
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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.

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Re: In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 30 Mar 2015, 06:16
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
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In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 30 Mar 2015, 10:43
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Bunuel 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.

Kudos for a correct solution.


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
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Re: In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 06 Apr 2015, 05:35
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Bunuel 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.

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
findn_exp.png
findn_exp.png [ 33.7 KiB | Viewed 1967 times ]

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Re: In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 12 Nov 2015, 19:06
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.

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Re: In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 15 Nov 2015, 10:48
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.
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Re: In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 06 Mar 2018, 11:50
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
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In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 18 May 2018, 18:42
Bunuel gmatbusters niks18 mvictor amanvermagmat

Quote:
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.


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.
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Re: In the rectangular coordinate system, line k is defined by the equatio [#permalink]

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New post 18 May 2018, 19:02
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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.

adkikani wrote:

Quote:
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.


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.

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Re: In the rectangular coordinate system, line k is defined by the equatio   [#permalink] 18 May 2018, 19:02
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