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Compare 80^1/3 and 270^1/3 -10^1/3

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1659 [0], given: 396

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Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink] New post 09 May 2016, 15:40
Expert's post
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Question Stats:

45% (00:41) correct 54% (01:05) wrong based on 35 sessions
Quantity A
Quantity B
\(80^{\frac{1}{3}}\)
\(270^{\frac{1}{3}}- 10^{\frac{1}{3}}\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




Practice Questions
Question: 2
Page: 62
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
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WE: Business Development (Energy and Utilities)
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Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink] New post 09 May 2016, 15:45
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Explanation

You can simplify both quantities. Quantity A can be simplified as follows:

\(80^1^/^3 = 8^1^/^3 * 10^1^/^3 = 2 *10^1^/^3\)

Quantity B can be simplified as follows:

\(270^1^/^3 - 10^1^/^3 = 27^1^/^3 *10^1^/^3 - 10^1^/^3= 3*10^1^/^3 - 10^1^/^3= 2 *10^1^/^3\)

Hence both Quantities are equal.
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Sandy
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Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink] New post 15 Jul 2016, 05:15
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sandy wrote:
Quantity A
Quantity B
\(80^{1/3}\)
\(270^1^/^3- 10^1^/^3\)




IMPORTANT RULE:(ab)^y = (a^y)(b^y)
For example, 12^17 = (4^17)(3^17)

Given:
Quantity A: 80^(1/3)
Quantity B: 270^(1/3) - 10^(1/3)

Apply law to get:
Quantity A: [10^(1/3)][8^(1/3)]
Quantity B: [27^(1/3)][10^(1/3)] - 10^(1/3)

Factor out 10^(1/3) in quantity B to get:
Quantity A: [10^(1/3)][8^(1/3)]
Quantity B: [10^(1/3)][27^(1/3) - 1]

Divide both quantities by 10^(1/3) to get:
Quantity A: 8^(1/3)
Quantity B: 27^(1/3) - 1

Evaluate both quantities to get:
Quantity A: 2
Quantity B: 3 - 1

Answer:
[Reveal] Spoiler:
C

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Brent Hanneson – Creator of greenlighttestprep.com
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Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink] New post 02 May 2018, 00:07
In one of the steps in Brent's solution, I didn't understand how the below Quantity B came to be. Can that be explained to me? Thanks.

Factor out 10^(1/3) in quantity B to get:
Quantity A: [10^(1/3)][8^(1/3)]
Quantity B: [10^(1/3)][27^(1/3) - 1]
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Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink] New post 02 May 2018, 05:17
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jen6 wrote:
In one of the steps in Brent's solution, I didn't understand how the below Quantity B came to be. Can that be explained to me? Thanks.

Factor out 10^(1/3) in quantity B to get:
Quantity A: [10^(1/3)][8^(1/3)]
Quantity B: [10^(1/3)][27^(1/3) - 1]


In the step before that, we have: Quantity B: [27^(1/3)][10^(1/3)] - 10^(1/3)

This similar to the expression xy - y
With this expression, we can factor out the y to get: xy - y = y(x - 1)

Likewise, in the original expression, we can factor out 10^(1/3) to get: [27^(1/3)][10^(1/3)] - 10^(1/3) = [10^(1/3)][27^(1/3) - 1]

Does that help?

Cheers,
Brent
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Re: Compare 80^1/3 and 270^1/3 -10^1/3   [#permalink] 02 May 2018, 05:17
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