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given 8z^4 = 96

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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given 8z^4 = 96 [#permalink] New post 02 Jul 2017, 15:31
Expert's post
00:00

Question Stats:

80% (00:55) correct 20% (01:00) wrong based on 20 sessions
\(8z^4 = 96\)

Quantity A
Quantity B
2
z


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

Drill 1
Question: 2
Page: 352
[Reveal] Spoiler: OA

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Re: given 8z^4 = 96 [#permalink] New post 06 Jul 2017, 05:50
Expert's post
sandy wrote:
\(8z^4 = 96\)

Quantity A
Quantity B
2
z




Given: \(8z^4 = 96\)

Divide both sides by 8 to get: \(z^4 = 12\)

So, EITHER z = ∜12 OR z = -∜12

Notice that ∜1 = 1 and ∜16 = 2. So ∜12 must be BETWEEN 1 and 2.

We can say ∜12 = 1.something and -∜12 = -1.something

Since 1.something and -1.something are both smaller than 2, we can conclude that Quantity A is greater.

Answer:
[Reveal] Spoiler:
A


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1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1611 [1] , given: 375

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Re: given 8z^4 = 96 [#permalink] New post 22 Apr 2018, 14:05
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Expert's post
Explanation

Divide both sides by 8 to get \(z^4 = 12\). Rather than finding the fourth root of 12, try plugging in 2 for z: \(2^4 = 16\), so z must be less than 2. Of course, z may be negative, but any negative number is also less than 2.

Hence option A is correct!
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Re: given 8z^4 = 96   [#permalink] 22 Apr 2018, 14:05
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given 8z^4 = 96

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