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

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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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BrentGMATPrepNow wrote:
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
-------------------------------------------------

Hi BrentGMATPrepNow,

Square root of x^2 can be either +x or -x. On the same lines, could you please explain why we ignored the negative possibilities in statement 2? If we were to assume there are 2 possibilities - positive and negative, statement 2 would have been insufficient. Please help.

Thanks,
Harshbir
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Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000 [#permalink]
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Bunuel wrote:
Is $$7^x > 100$$ ?

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

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

Are You Up For the Challenge: 700 Level Questions

$$7^x > 100$$..

(1) $$7^{(x+2)} > 9,800........7^x*7^2>9800......7^x*49>9800.......7^x>200>100.......7^x>100$$
Yes and sufficient

(2) $$7^{(2x)} > 10,000....(7^x)^2>100^2........7^x>100$$
Yes and sufficient

D

harshbirsingh, on your query that $$7^x<-100$$ should also be checked.
$$7^x$$ can never be negative. Even if x is some negative quantity to the tune of say -10000000, $$7^{-10000000}=\frac{1}{7^{10000000}}>0$$, so $$7^x<-100$$ is NOT valid.
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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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harshbirsingh wrote:

Square root of x^2 can be either +x or -x. On the same lines, could you please explain why we ignored the negative possibilities in statement 2? If we were to assume there are 2 possibilities - positive and negative, statement 2 would have been insufficient. Please help.

Thanks,
Harshbir

Since the base, 7, is positive, we can be certain that 7^x is positive for all values of x.
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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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Re: Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000 [#permalink]
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