In the rectangular coordinate system above, the shaded region is bound

Question

https://gmatclub.com/forum/download/file.php?id=21944 In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s? (A) x = 0 (B) y = 0 (C) x = 1 (D) x - y = 0 (E) x + 2y = 2 Untitled.png

abhimahna · Accepted Answer

I did this question in hardly 10 seconds and would love to share my approach.

We need to find out which of the equations given isn't a part of the shaded figure given.

Let's pick options:

(A) x = 0 ==>  This is y axis. We do have y axis a part of our figure. Hence, OUT. 
(B) y = 0 ==>  This is x axis. We do have x axis a part of our figure. Hence, OUT. 
(C) x = 1 ==>  This is line || to y axis and passing through x = 1. We do have that vertical line. Hence, OUT.
 (D) x - y = 0 ==>  This is x = y. This means we have a line passing through the origin and for every value of x, we have the same value of y. I don't see any such line. 
(E) x + 2y = 2 ==>  Put y = 0, x = 2. And when x= 0, y = 1; We do have that as a part of the shaded figure. Hence, OUT.

Only option that remains is D. Hence, the correct answer.

Does that make sense?

WoundedTiger · Answer

In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s?

(A) x = 0
(B) y = 0
(C) x = 1
(D) x - y = 0
(E) x + 2y = 2

Attachment:

untitled2.PNG [ 9.45 KiB | Viewed 47417 times ]

Sol:We need to find the which of the lines is not represented in the graph given.

It is easier to point out that ans is D because x=y is a line at 45 degree to X -axis and there is no line passing as can be seen in the graph. Let's see if we can confirm

X=0 (Y-Axis) and X=1 are vertical lines so Option A and C ruled out
Y=0 is the horizontal line (X-axis)

Equation of the line with points of intersection (0,1) and (2,0)

Slope of the line = (y2-y1)/(x2-x1)-----> (1-0)/(0-2) ie. -1/2
The Y intercept form of line is given by y=mx+c where m is the slope (we calculated) and c is the y intercept when x=0 and we know C is 1
Thus y=-1/2x+1-------> x+2y=2, Hence E is ruled out.

Ans is D

kinjiGC · Answer

x= 0 and y = 0 are both y and x axis respectively so definitely those lines are there.
x = 1 is the line is parallel to y axis.
Now if we see there is a line which satisfies y = 1 when x =0 (that is on y axis) and x = 2 when y = 0 (that is on x axis), so only equation which satisfies both is x + 2y = 2.
Hence Option D) is the equation which is not present.

kundankshrivastava · Answer

Following points should be remembered:

equation of x axis => y = 0
equation of y axis => x = 0
equation of a line parallel to y axis and passing through x axis at a => x = a
equation of a line parallel to x axis and passing through y axis at a => y = a
equation of a line cutting x axis at a and y axis at b => (x/a) + (y/b) =1

Attachment:

File comment: equation of line

gmatcoordinate.jpg [ 22.12 KiB | Viewed 17187 times ]

Shaded region is surrounded by the following

x axis => y = 0
y axis => x = 0
a line parallel to y axis and crossing x axis at 1 => x = 1
a line crossing x axis at 2 and y axis at 1 => (x/2) + (y/1) = 1 => x + 2y = 2

Out of the given options only x-y = 0 is not the equation of a boundary line.. Hence Answer is D

amz14 · Answer

Definitely D.

x-y=0 ; x=y is a line with a positive slope going through the origin.

NoHalfMeasures · Answer

x = 0, x = 1 are two vertical lines so they are ruled out. 
 y = 0 is x-axis so ruled out
Left with these two choice
(D) x - y = 0
(E) x + 2y = 2

looking at the remaining line in the figure we know that the slope is negative. D is y=x has positive slope so thats the answer

gracie · Answer

x-y=0➡y=x
equation y=x has a positive slope of 1 and runs through the origin at a 45° angle 
not a boundary line
D

JeffTargetTestPrep · Answer

The vertical line on the left (which is also the y-axis) has the equation of x = 0.

The vertical line on the right has the equation of x = 1.

The horizontal line at the bottom (which is also the x-axis) has the equation of y = 0.

The diagonal line at the top has the equation of y = (-½)x + 1. When simplifying answer choice E, we see that we have that same equation:

x + 2y = 2

2y = -x + 2

y = (-½)x + 1

Thus, the correct answer is D.

Answer: D

generis · Answer

Answer E accounts for the vast majority of incorrect answers.

See below, the correct answer is D or E.
A, B, and C contain equations for the vertical and horizontal lines.*

The equation of the boundary line with a slope must be D or E.

Plug in  coordinates  
• From the graph, we have (0,1) and (2,0)
• Known coordinates will make the line's equation true.

Plug (2,0) into D and E. 
One result will be false, and hence NOT an equation of a boundary line.

(D)  x - y = 0 :

2 - 0=2 
 2
eq0  FALSE
 x-y=0  is NOT the equation of the sloped boundary line

(E)  x + 2y = 2 :

2+(2*0)=2  
 2=2 . TRUE
This equation IS the equation of the sloped line

Answer D

A, B, and C contain the line equations of the vertical and horizontal boundaries. Eliminate all. Eliminate 
-- A (one vertical side lies on the y-axis, i.e. x = 0) 
-- B (the horizontal side lies on the x-axis, i.e., y = 0) and 
-- C (the other vertical side lies on x = 1)

AyushCrackVerbal · Answer

Since X and Y axis are the boundary lines of the shaded region, x=0 and y=0 are the boundary line equations. Options A and B cannot be the answer

Since a line parallel to Y-axis and passing through (1,0) is also the boundary line, x=1 is the boundary line equation. Option C cannot be the answer

Equation x-y=0 can be written as x=y. The line x=y passes through the origin (0,0) and (1,1) and so on. We can clearly see that no boundary line passes through (1,1). Hence D is the answer.

One of the boundary lines passes through (0,1) and (2,0). To find the equation of a line passing through the given two points:

y = mx + c, where m is the slope of the line and c is the constant.

m = (y coordinate of the second point- y coordinate of the first point) / (x coordinate of the second point - x coordinate of the first point)

m = (0-1) / (2-0) = -1/2

y = (-1/2)x + c

Since the equation passes through the point (0,1). Put x=0 and y=1 to find the value of c:

1 = (-1/2)*0 + c

c = 1

y = -x/2 + 1

2y = -x + 2

x + 2y = 2

Therefore E cannot be the answer.

The correct answer is  D

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

In the rectangular coordinate system above, the shaded region is bound

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 rectangular coordinate system above, the shaded region is bound

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