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505-555 (Easy)|   Geometry|               
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KarishmaB
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A six-sided mosaic contains 24 triangular pieces of tile of the same 09 Oct 2022, 07:32
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Tanchat
Dear Experts, KarishmaB Bunuel BrentGMATPrepNow and ScottTargetTestPrep and others

1) Is it possible that other types of Triangle can form this six-sided mosaic?

2) in the statement two, if the first question is NO, do we actually require the length of triangle? We know the wide of rectangle and the mosaic can be put into the rectangle, we definitely know the size of the triangle.

3) According to the statement two, (2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.
can we imply that the mosaic perfectly fits into the rectangular? or it is possible that this rectangular may be larger than the mosaic --> so the mosaic can be put into the rectangular but we cannot define any size of the mosaic (or triangle)

Thank you in advance
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Stmnt 1 gives us that the triangles are equilateral but think about what happens in case of isosceles triangles. Imagine that the horizontal base of each triangle is just 6 cm while other two sides are still 9 cm each. Will we face any problem in making the mosaic?

Stmtn 2 means that the mosaic fits into a 40 cms wide frame so its width is less than or equal to 40 cm. It is not necessary that its width is exactly 40 cm.
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A six-sided mosaic contains 24 triangular pieces of tile of the same 09 Oct 2022, 10:48
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KarishmaB
Tanchat
Dear Experts, KarishmaB Bunuel BrentGMATPrepNow and ScottTargetTestPrep and others

1) Is it possible that other types of Triangle can form this six-sided mosaic?

2) in the statement two, if the first question is NO, do we actually require the length of triangle? We know the wide of rectangle and the mosaic can be put into the rectangle, we definitely know the size of the triangle.

3) According to the statement two, (2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.
can we imply that the mosaic perfectly fits into the rectangular? or it is possible that this rectangular may be larger than the mosaic --> so the mosaic can be put into the rectangular but we cannot define any size of the mosaic (or triangle)

Thank you in advance

Stmnt 1 gives us that the triangles are equilateral but think about what happens in case of isosceles triangles. Imagine that the horizontal base of each triangle is just 6 cm while other two sides are still 9 cm each. Will we face any problem in making the mosaic?

Stmtn 2 means that the mosaic fits into a 40 cms wide frame so its width is less than or equal to 40 cm. It is not necessary that its width is exactly 40 cm.
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KarishmaB

Thank you for your response and explanation :)

I have further questions

I'm not sure whether isosceles triangles can be fit here. To be honest, I am not familiar with Geometry. How can I check that isosceles triangles can be combined to develop the six-sided mosaic?

For statements 2, if we want to convey the meaning that the mosaic width is exact 40 cm. the question will clear tell us, right? It can be "inscribed", or "exactly fit".
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A six-sided mosaic contains 24 triangular pieces of tile of the same 19 Oct 2022, 13:51
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GMATinsight
Bunuel

A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?

(1) Each side of each triangular piece of tile is 9 centimeters long.
(2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.


DS24602.01
OG2020 NEW QUESTION


Show Spoiler
Attachment:
2019-04-26_1400.png

Answer: Option A

Video solution by GMATinsight

Show more

Hi GMATinsight

I disagree with the last part of your explanation in the video i.e. you told: "for 2nd statement if it has been mentioned the mosaic exactly fits in the rectangle of width 40 cm then the statement would be sufficient"

Why I disagree:
Because then also it depends on how we are putting mosaic in the rectangle, there will be multiple possibilities for ex: 40== 4* length of each tile
OR
40 ==4* height of the equilateral triangle (if u have assumed tiles to be in the shape of equilateral triangle)
In both cases you will get different value of mosaic side.

I may be wrong hence requesting your reply on this please

Thank you
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A six-sided mosaic contains 24 triangular pieces of tile of the same 20 Oct 2022, 01:10
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760Abhi
GMATinsight
Bunuel

A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?

(1) Each side of each triangular piece of tile is 9 centimeters long.
(2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.


DS24602.01
OG2020 NEW QUESTION


Show Spoiler
Attachment:
2019-04-26_1400.png

Answer: Option A

Video solution by GMATinsight


Hi GMATinsight

I disagree with the last part of your explanation in the video i.e. you told: "for 2nd statement if it has been mentioned the mosaic exactly fits in the rectangle of width 40 cm then the statement would be sufficient"

Why I disagree:
Because then also it depends on how we are putting mosaic in the rectangle, there will be multiple possibilities for ex: 40== 4* length of each tile
OR
40 ==4* height of the equilateral triangle (if u have assumed tiles to be in the shape of equilateral triangle)
In both cases you will get different value of mosaic side.

I may be wrong hence requesting your reply on this please

Thank you
Show more

Hi 760Abhi

Yes, you are right however that's not a disagreement, it's another added information needed alongwith the infomation of perfectly filling mosaic in rectangle of width 40.

:) :thumbsup:
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A six-sided mosaic contains 24 triangular pieces of tile of the same 01 Nov 2023, 05:18
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