GMAT Math : DSQ: Calculating the length of an edge of a tetrahedron

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Example Question #1 : Dsq: Calculating The Length Of An Edge Of A Tetrahedron

Find the length of the edge of a tetrahedron.

Statement 1: The volume is 6.

Statement 2: The surface area is 6.

Possible Answers:

$\textup{EACH statement ALONE is sufficient.}$

$\textup{Statement 2) ALONE is sufficient, but Statement 1) ALONE is not sufficient to answer the question.}$

$\textup{BOTH statements taken TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient.}$

$\textup{Statement 1) ALONE is sufficient, but Statement 2) ALONE is not sufficient to answer the question.}$

$\textup{BOTH statements TOGETHER are NOT sufficient, and additional data is needed to answer the question. }$

Correct answer:

$\textup{EACH statement ALONE is sufficient.}$

Explanation:

Statement 1:) The volume is 6.

Write the formula to find the edge of the tetrahedron given the volume.

$V=\frac{e^3}{6\sqrt2}$

Given the volume, it is possible to find the edge of the tetrahedron.

Statement 2:) The surface area is 6.

Write the formula to find the edge of the tetrahedron given the surface.

$SA=\sqrt3 e^2$

Substitute the surface area to find the edge.

Therefore:

$\textup{EACH statement ALONE is sufficient.}$

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GMAT Math : DSQ: Calculating the length of an edge of a tetrahedron

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Example Question #1 : Dsq: Calculating The Length Of An Edge Of A Tetrahedron

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