GMAT Math : DSQ: Calculating the diagonal of a prism

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Example Question #1 : Dsq: Calculating The Diagonal Of A Prism

Find the length of the diagonal of cube GHOU $\displaystyle GHOU$.

I) GHOU $\displaystyle GHOU$ has a volume of 343cm^3 $\displaystyle 343cm^3$.

II) GHOU $\displaystyle GHOU$ has a surface area of 294cm^2 $\displaystyle 294cm^2$.

Possible Answers:

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Both statements are needed to answer the question.

Correct answer:

Either statement is sufficient to answer the question.

Explanation:

To find the length of the diagonal, we need the side length.

I) Gives us the volume of the cube. Take the cubed root to find the side length.

$V=s^3 \rightarrow 343=s^3 \rightarrow =7$ $\displaystyle V=s^3 \rightarrow 343=s^3 \rightarrow =7$

II) Gives us the surface area, divide by 6 (the number of faces in a cube) and take the square root to find the side length.

$SA=6s^2 \rightarrow 294=6s^2$ $\displaystyle SA=6s^2 \rightarrow 294=6s^2$

$49=s^2 \rightarrow 7=s$ $\displaystyle 49=s^2 \rightarrow 7=s$

Diagonal of a cube is the side length times the square root of three. Alternatively, this can be found using the Pythagorean Theorem twice.

Either way, we can use I) or II) to find our side lenght and then our diagonal.

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Example Question #73 : Rectangular Solids & Cylinders

What is the diagonal of a rectangular prism?

1) Its surface area is 48 in^2 $\displaystyle 48 in^2$

2) Its height = twice its width = thrice its length.

Possible Answers:

Neither of the statements, separate or together, is sufficient.

Statement 2 alone is sufficient.

Together, the two statements are sufficient.

Either of the statements is sufficient.

Statement 1 alone is sufficient.

Correct answer:

Together, the two statements are sufficient.

Explanation:

The diagonal of a rectangular prism is found via the formula $\sqrt{w^2+l^2+h^2}$ $\displaystyle \sqrt{w^2+l^2+h^2}$

The second statement reduces this to $\sqrt{(3l)^2+l^2+(6l)^2}=\sqrt{46l^2}$ $\displaystyle \sqrt{(3l)^2+l^2+(6l)^2}=\sqrt{46l^2}$

However, the actual length is unknown. Statement 1 allows the calculation of a numerical value:

$\displaystyle 2wl+2wh+2lh=48in^2$

$\displaystyle 2(3l)(l)+2(3l)(6l)+2(l)(6l)=48in^2$

$\displaystyle 6l^2+36l^2+12l^2=48in^2$

$l^2=\frac{48}{54}in^2$ $\displaystyle l^2=\frac{48}{54}in^2$

$l=\sqrt{\frac{8}{9}}in$ $\displaystyle l=\sqrt{\frac{8}{9}}in$

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GMAT Math : DSQ: Calculating the diagonal of a prism

Study concepts, example questions & explanations for GMAT Math

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Example Question #1 : Dsq: Calculating The Diagonal Of A Prism

Example Question #73 : Rectangular Solids & Cylinders

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