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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 , given: 397

Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink]
Expert's post 00:00

Question Stats: 37% (00:44) correct 62% (01:27) wrong based on 45 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

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782  , given: 397

Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink]
1
KUDOS
Expert's post
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.
_________________

Sandy
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Try our free Online GRE Test GRE Instructor Joined: 10 Apr 2015
Posts: 1539
Followers: 56

Kudos [?]: 1464  , given: 8

Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink]
2
KUDOS
Expert's post
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

[Reveal] Spoiler:
C

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails

Intern Joined: 17 Mar 2018
Posts: 9
Followers: 0

Kudos [?]: 2 , given: 7

Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink]
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] GRE Instructor Joined: 10 Apr 2015
Posts: 1539
Followers: 56

Kudos [?]: 1464  , given: 8

Re: Compare 80^1/3 and 270^1/3 -10^1/3 [#permalink]
2
KUDOS
Expert's post
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
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Re: Compare 80^1/3 and 270^1/3 -10^1/3   [#permalink] 02 May 2018, 05:17
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