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Isn't geometry not being tested? why is it being asked here?

I got this wrong because I am trying to imagine how'd a parallelogram have all vertices lied on both X and Y axsis.
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Isn't geometry not being tested? why is it being asked here?

I got this wrong because I am trying to imagine how'd a parallelogram have all vertices lied on both X and Y axsis.


Exactly, there is no way a parallelogram can be made using x axis and y axis unless opposite vertices lie on the same axis.
Just substitute x=0, to get those y-coordinates, and vice versa.
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Can you please add the tag Coordinate Geometry please?
Thank you :)
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PFA the grpahical representation of this problem. GMATinsight chetan2u
Attachments

grpah_17th.png
grpah_17th.png [ 33.45 KiB | Viewed 8060 times ]

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Here is my approach, take around 2mins

We have 4 situations:
3x + 7y = 21 (1)
3x - 7y = 21 (2)
-3x +7y =21 (3)
-3x - 7y = 21 (4)

So, let sum (1) and (2) => 6x = 42, => x= 7
let sum (1) and (3) => 14y = 42 => y =3

Double both get the answer H = 2x = 14, and V = 2y = 6
yikes000
In the standard (x,y) coordinate plane, the graph of \(|3x| + |7y| = 21\) is a parallelogram with 2 vertices on the x-axis and 2 vertices on the y-axis. Let H and V be the lengths, in coordinate units, of the horizontal and vertical diagonals, respectively, of this parallelogram.

Select for H and for V values that are consistent with the given information. Make only two selections, one in each column.

Attachment:
DI -3.png
­
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1. It's always better to visualize the problem: the parallelogram, H, and V. We are asked to find H and V.



2. Note that the figure must be centered at (0,0) since if (x,y) is a solution, then so is (-x,y), (x,-y), and (-x,-y).

3. To find H and V we need to find the coordinates of the vertices. Let them be (x,0), (-x,0), (0,y), and (0,-y). Also let x and y be positive.

4. Now let's add the condition that each of these points must work in the equation: \(|3x| + |7y| = 21\).

  • (x,0). \(|3x| + |7y| = 21 \rightarrow 21 = |3 * x| + |7 * 0| = |3x| \rightarrow x = \pm 7\). Since x > 0, x = 7 and the point is (7,0).

  • (-x,0). This case is the same as (x,0) but the point will be (-7,0).

  • (0,y). \(|3x| + |7y| = 21 \rightarrow 21 = |3 * 0| + |7 * y| = |7y| \rightarrow y = \pm 3\). Since y > 0, y = 3 and the point is (0,3).

  • (0,-y). This case is the same as (0,y) but the point will be (0,-3).

5. Based on the image, H = 2x and V = 2y. So, H\( = 14\) and V\( = 6\).

Attachment:
ParallelogramGraph.jpg
ParallelogramGraph.jpg [ 29.6 KiB | Viewed 6198 times ]
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yikes000
In the standard (x,y) coordinate plane, the graph of \(|3x| + |7y| = 21\) is a parallelogram with 2 vertices on the x-axis and 2 vertices on the y-axis. Let H and V be the lengths, in coordinate units, of the horizontal and vertical diagonals, respectively, of this parallelogram.

Select for H and for V values that are consistent with the given information. Make only two selections, one in each column.

Attachment:
DI -3.png
­

The question involves some graphing knowledge, some basic knowledge about shapes (what is a parallelogram? As long as you know it is a 4 sides closed figure, that's enough) and some basic absolute values concepts. Overall, it is typical GMAT question - involves multiple areas but is simple.

Graph of \(|x| + |y| = a\) is a closed 4 sided figure around (0, 0) with diagonals on X and Y axis.

I discussed graphing this in this video on YouTube: https://youtu.be/dPwGi8oV9ns

Even if we do not know this, we are given that 2 vertices are on X axis and 2 are on Y axis and H and V are the diagonals. Then the diagonals must be on X and Y axis. All we need to do is find the points on the axis to get the lengths of the diagonals.

\(|3x| + |7y| = 21\)

On Y axis, x = 0 so |7y| = 21
y = 3 or -3
Length of vertical diagonal V = 6

On X axis, y = 0 so |3x| = 21
x = 7 or -7
Length of horizontal diagonal H = 14

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