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Is x^4 > 2,000?

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Is x^4 > 2,000?  [#permalink]

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New post 20 Nov 2016, 09:26
1
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A
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D
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Difficulty:

  55% (hard)

Question Stats:

71% (02:26) correct 29% (01:58) wrong based on 68 sessions

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Re: Is x^4 > 2,000?  [#permalink]

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New post 20 Nov 2016, 09:37
1
Bunuel wrote:
Is x^4 > 2,000?

(1) x^3 > 400

(2) x > 7.25


from 1 we know:
x^3 > 2^4 * 5^2
7^3 = 343
8^3 = 512
x must be greater than 7 100%.
7^4 = 2401 - so already sufficient.

2. sufficient. if x=7, then it is already sufficient.

D is the answer.
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Re: Is x^4 > 2,000?  [#permalink]

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New post 20 Nov 2016, 09:55
1
Bunuel wrote:
Is x^4 > 2,000?

(1) x^3 > 400

(2) x > 7.25



IMO D

From statement 1
x^3 > 400
6^3= 216, 7^3= 343 8^3= 512
so x must be greater than 7
7^4= 2401,
Yes, Sufficient

From statement 2
x > 7.25
so x^4 > 2762.8
Hence sufficient

Hence D
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Re: Is x^4 > 2,000?  [#permalink]

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New post 20 Nov 2016, 12:47
mvictor wrote:
Bunuel wrote:
Is x^4 > 2,000?

(1) x^3 > 400

(2) x > 7.25


from 1 we know:
x^3 > 2^4 * 5^2
7^3 = 343
8^3 = 512
x must be greater than 7 100%.
7^4 = 2401 - so already sufficient.

2. sufficient. if x=7, then it is already sufficient.

D is the answer.


Exactly.
Answer is D as mvictor explained!
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Is x^4 > 2,000?  [#permalink]

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New post 20 Nov 2016, 19:58
Bunuel wrote:
Is x^4 > 2,000?

(1) x^3 > 400

(2) x > 7.25



(1) \(x^3 >400\)

We have \(7^3=343\), so \(x^3 >400 >343 = 7^3\) or \(x>7\).
Hence, \(x^4 > 7^4 = 49^2 = 2401 > 2000\), sufficient

(2) We have \(x>7.25>7\) . Hence \(x^4 >7^4 >2000\), sufficient.

The answer is D
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Re: Is x^4 > 2,000?  [#permalink]

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New post 12 Dec 2017, 12:33
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Re: Is x^4 > 2,000? &nbs [#permalink] 12 Dec 2017, 12:33
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