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605-655 (Medium)|   Geometry|      
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Bunuel
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 01 Jul 2022, 13:15
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio of length to width to height of 4 : 3 : 2. In terms of n, which of the following equals the length of the cuboid, in feet?


A. \(\sqrt[3]{\frac{n}{8}}\)

B. \(2*\sqrt[3]{\frac{n}{3}}\)

C. \(\frac{1}{2}*\sqrt[3]{\frac{n}{3}}\)

D. \(\sqrt[3]{\frac{n}{3}}\)

E. \(8*\sqrt[3]{\frac{n}{3}}\)
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B
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 01 Jul 2022, 15:05
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Powers and rites rules are important to be agile at the GMAT
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 01 Jul 2022, 21:11
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Bunuel
A cuboid (rectangular solid) has a volume of n cubic feet and a ratio of length to width to height of 4 : 3 : 2. In terms of n, which of the following equals the length of the cuboid, in feet?


A. \(\sqrt[3]{\frac{n}{8}}\)

B. \(2*\sqrt[3]{\frac{n}{3}}\)

C. \(\frac{1}{2}*\sqrt[3]{\frac{n}{3}}\)

D. \(\sqrt[3]{\frac{n}{3}}\)

E. \(8*\sqrt[3]{\frac{n}{3}}\)
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n?!?!? Why would we work in terms of n when we could just plug in dimensions? Let's just make them 4x3x2. The volume is 24. n = 24. Length = 4.

Check the answer choices.

A. \(\sqrt[3]{3}\) Nope.

B. \(2*\sqrt[3]{8}\) Keep it.

C, D, and E are just different multiples of \(\sqrt[3]{8}\) Nope.

Answer choice B.
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 02 Jul 2022, 14:49
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Bunuel
A cuboid (rectangular solid) has a volume of n cubic feet and a ratio of length to width to height of 4 : 3 : 2. In terms of n, which of the following equals the length of the cuboid, in feet?


A. \(\sqrt[3]{\frac{n}{8}}\)

B. \(2*\sqrt[3]{\frac{n}{3}}\)

C. \(\frac{1}{2}*\sqrt[3]{\frac{n}{3}}\)

D. \(\sqrt[3]{\frac{n}{3}}\)

E. \(8*\sqrt[3]{\frac{n}{3}}\)


n?!?!? Why would we work in terms of n when we could just plug in dimensions? Let's just make them 4x3x2. The volume is 24. n = 24. Length = 4.

Check the answer choices.

A. \(\sqrt[3]{3}\) Nope.

B. \(2*\sqrt[3]{8}\) Keep it.

C, D, and E are just different multiples of \(\sqrt[3]{8}\) Nope.

Answer choice B.
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Great! But I have a question: how the candidate goes from length 4 to one of the options a,b,c,d or e?
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 02 Jul 2022, 15:26
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Bunuel
A cuboid (rectangular solid) has a volume of n cubic feet and a ratio of length to width to height of 4 : 3 : 2. In terms of n, which of the following equals the length of the cuboid, in feet?


A. \(\sqrt[3]{\frac{n}{8}}\)

B. \(2*\sqrt[3]{\frac{n}{3}}\)

C. \(\frac{1}{2}*\sqrt[3]{\frac{n}{3}}\)

D. \(\sqrt[3]{\frac{n}{3}}\)

E. \(8*\sqrt[3]{\frac{n}{3}}\)


n?!?!? Why would we work in terms of n when we could just plug in dimensions? Let's just make them 4x3x2. The volume is 24. n = 24. Length = 4.

Check the answer choices.

A. \(\sqrt[3]{3}\) Nope.

B. \(2*\sqrt[3]{8}\) Keep it.

C, D, and E are just different multiples of \(\sqrt[3]{8}\) Nope.

Answer choice B.

Great! But I have a question: how the candidate goes from length 4 to one of the options a,b,c,d or e?
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We have n = 24 and length = 4. So we can plug n = 24 into each of the answer choices (well, we never really have to do C, D, or E because we can see that they won't work) to see which results in 4.
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 01 Nov 2022, 04:03
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Can you please explain more on how \(2*\sqrt[3]{8}\) = 4.
its 8*3=24*2=48?
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A cuboid (rectangular solid) has a volume of n cubic feet and a ratio 01 Nov 2022, 05:43
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omema
Can you please explain more on how \(2*\sqrt[3]{8}\) = 4.
its 8*3=24*2=48?
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Are you certain that \(\sqrt[3]{8}\) means 8*3?

Brush up on roots and exponents!

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