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

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Math Expert
Joined: 02 Sep 2009
Posts: 60480
Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000  [#permalink]

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05 Nov 2019, 06:10
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Difficulty:

45% (medium)

Question Stats:

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

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Is $$7^x > 100$$ ?

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

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

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Posts: 4214
Re: Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000  [#permalink]

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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

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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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.

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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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