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Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000

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Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000  [#permalink]

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New post 05 Nov 2019, 06:10
1
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (01:39) correct 28% (01:42) wrong based on 64 sessions

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Re: Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000  [#permalink]

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New post 05 Nov 2019, 06:55
Top Contributor
Bunuel wrote:
Is \(7^x > 100\) ?


(1) \(7^{(x+2)} > 9,800\)

(2) \(7^{(2x)} > 10,000\)



Target question: Is \(7^x > 100\)

Statement 1: \(7^{(x+2)} > 9,800\)
Rewrite as: \((7^x)(7^2) > 9,800\)
In other words: \((7^x)(49) > 9,800\)
Divide both sides by 49 to get: \((7^x) > 200\)
Since 200 > 100, we can write: \((7^x) > 200 >100\)
So, the answer to the target question is YES, 7^x IS greater than 100
Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Statement 2: \(7^{(2x)} > 10,000\)
Rewrite as: \((7^x)^2 > 100^2\)
This means: \(7^x > 100\)
The answer to the target question is YES, 7^x IS greater than 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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Re: Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000  [#permalink]

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New post 05 Nov 2019, 10:21
1
Is \(7^x > 100\) ?
Since \(7^3 = 343\), is x > 2 ?

(1) \(7^{x+2} > 9,800\)
\(7^x . 7^2 > 9800\)
\(7^x > 200\) (dividing both sides by 7^2)
x > 2

SUFFICIENT.

(2) \(7^{2x} > 10,000\)
Taking square root
\(7^x > 100\)
x >2

SUFFICIENT.

Answer D.
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Re: Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000   [#permalink] 05 Nov 2019, 10:21
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