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A six-sided mosaic contains 24 triangular pieces of tile

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A six-sided mosaic contains 24 triangular pieces of tile

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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?

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

A

Source: Official Guide 2020

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If we know each triangle is equilateral with sides of length 9, and we know how many triangles we have, of course we can find the area of all of them, so Statement 1 is sufficient.

That we can fit the mosaic in some rectangle limits how large the mosaic might be, but we have no idea how much empty space will surround the mosaic within the rectangular frame - the mosaic could be microscopic, or could be a foot wide, so we can't answer the question using Statement 2.

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Hi All,

We're told that a six-sided mosaic contains 24 triangular pieces of tile of the SAME size and shape, as shown in the figure above and that the sections of tile fit together perfectly. We're asked for the total square centimeters of tile in the mosaic. While this question might look a bit 'crazy', it's a great "concept question" meaning that if you know the concepts involved, then you won't have to do much math to actually get the correct answer. To answer this question, we'll need information to determine the area of any one of the triangles, then we can multiply that area by 24 to get the total area of the mosaic.

1) Each side of each triangular piece of tile is 9 centimeters long.

Fact 1 tells us that we're dealing with Equilateral triangles with sides of 9 cm. With this information, we can determine the area of each triangular tile (the best part is that we don't actually have to do that math here; we know that we CAN do that math - and that there will be just one value for the area - so we can stop working).
Fact 1 is SUFFICIENT

2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.

The information in Fact 2 puts a limit on what the maximum side of each triangle could be, but doesn't given us any data on the exact areas involved, so since the triangles don't have a set area, the answer to the question will change as the areas change.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

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