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GRE Math Challenge #136 - XQY and ZYR are equilateral triang

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sandy
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GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   Updated on: 20 Feb 2020, 16:20
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Image

XQY and ZYR are equilateral triangles, and the ratio of ZR to PR is 1 to 4.

Quantity A
Quantity B
The perimeter of △XQY
The perimeter of parallelogram PXYZ


A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Show: ::
Attachment:
Quant8.jpg
Quant8.jpg [ 8.33 KiB | Viewed 13864 times ]
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A

Originally posted by sandy on 15 May 2015, 11:38.
Last edited by Carcass on 20 Feb 2020, 16:20, edited 4 times in total.
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greMS15
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Re: GRE Math Challenge #136- Geometry of Triangle [#permalink] New post   25 Nov 2015, 13:31
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i got the answer A . what is the correct answer ? it says E which is incorrect
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Re: GRE Math Challenge #136- Geometry of Triangle [#permalink] New post   28 Nov 2015, 12:36
what is the answer and how did u get?
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Re: GRE Math Challenge #136- Geometry of Triangle [#permalink] New post   29 Nov 2015, 05:19
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If the triangle ZRY and XQY are equilater and in the ration 1:4 we can conclude that YR is 2 for instance and XQ is 6.

As such, PX is 2 and XQ is 6. the perimeter XQY is 18. ZR is 2 and its perimeter is 6.

PZ is 6, YZ is 2, so the perimeter PXYZ is 16

The quantity A is greater. So the answer is A
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   09 Jun 2019, 13:16
could you give another explanation ?
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   09 Jun 2019, 13:43
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Attachment:
#GREpracticequestion XQY and ZYR are equilateral triang.png
#GREpracticequestion XQY and ZYR are equilateral triang.png [ 46.84 KiB | Viewed 8850 times ]


Hope this helps
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   12 Jun 2019, 22:24
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sandy wrote:
Image

XQY and ZYR are equilateral triangles, and the ratio of ZR to PR is 1 to 4.

Quantity A: The perimeter of △XQY
Quantity B: The perimeter of parallelogram PXYZ

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined


Show: ::
Attachment:
Quant8.jpg


-------------CONCEPT----------
Let ZR = x, so PR = 4x & PZ = 3x
Hence XY = 3x as well (parallelogram's opposite sides).

Now Perimeter of triangle XQY = 3*3x = 9x
Perimeter of Parallelogram PXYZ = x + 3x + x + 3x = 8x

Hence A (perimeter of triangle) is bigger
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   04 Sep 2019, 15:14
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sandy wrote:
Image

XQY and ZYR are equilateral triangles, and the ratio of ZR to PR is 1 to 4.

Quantity A
Quantity B
The perimeter of △XQY
The perimeter of parallelogram PXYZ



Show: ::
Attachment:
Quant8.jpg


GIVEN: the ratio of ZR to PR is 1 to 4.

If we let ZR have length 1, then PR must have length 4, which means PZ = 3
Image



If ZR = 1, and ZYR is an equilateral triangle, we know that all 3 sides have length 1
Image



If PZ = 3, and PXYZ is a parallelogram, we know that side XY = 3 (opposite sides of a parallelogram have equal lengths.
Likewise, since YZ = 1, we know that XP = 1
Finally, since XQY is an equilateral triangle, QY = 3 and QX = 3
Image



So, the perimeter of △XQY = 3 + 3 + 3 = 9
Image



And the perimeter of parallelogram PXYZ = 3 + 1 + 3 + 1 = 8
Image

We get:
QUANTITY A: 9
QUANTITY B: 8

Answer: A

Cheers,
Brent
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   06 Sep 2019, 20:39
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If the triangle ZRY and XQY are equilater and in the ration 1:4 we can conclude that YR is 2 for instance and XQ is 6.

As such, PX is 2 and XQ is 6. the perimeter XQY is 18. ZR is 2 and its perimeter is 6.

PZ is 6, YZ is 2, so the perimeter PXYZ is 16

The quantity A is greater. So the answer is A
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   18 Aug 2020, 13:14
Carcass wrote:
Attachment:
#GREpracticequestion XQY and ZYR are equilateral triang.png


Hope this helps




Not quite the right picture b/c your ZR/PR = 1/5 and not 1/4
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink] New post   03 Jul 2024, 05:57
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Re: GRE Math Challenge #136 - XQY and ZYR are equilateral triang [#permalink]
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