In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two poin

Question

In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5, then k =

A. 1/2
B. 1
C. 2
D. 5/2
E. 4

Kinshook · Answer

Asked: In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5, then k =

m = 2n + 5 (1)
m+2 = 2(n+k) + 5 (2)

(2) - (1) 
2 = 2k 
k = 1

IMO B

ScottTargetTestPrep · Answer

First, notice that the given linear equation is not in standard y = mx + b form because the x and y variables have been interchanged in x = my + b. With that said, we can create the following equations:

m = 2n + 5

and

m + 2 = 2(n + k) + 5

m + 2 = 2n + 2k

Substituting, we have:

2n + 5 + 2 = 2n + 2k + 5

2 = 2k

1 = k

Answer: B

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • In the xy-coordinate system, (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5

To find  
We need to determine
 • The value of k

Approach and Working out  
As (m, n) lies on the line x = 2y + 5, we can write
 • m = 2n + 5

Also, (m + 2, n + k) lies on the line x = 2y + 5. Hence, we can write
 • m + 2 = 2n + 2k + 5
Or, 2n + 5 + 2 = 2n + 2k + 5
Or, 2k = 2
Or, k = 1

Thus, option B is the correct answer.

Correct Answer: Option B

takozzz · Answer

Let's assume the slope of equation x= 2y + 5 is S, and we know S=1/2 (1)
Because (m, n) and (m + 2, n + k) are two points on the line, so we have 
S=(n+k-n)/(m+2-m) =k/2. (2)
So(1)+(2), k/2=1/2, k=1

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two poin

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two poin

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards