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# Is 7^(x + 2)/49 > 1 ?

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Math Expert
Joined: 02 Sep 2009
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Is 7^(x + 2)/49 > 1 ?  [#permalink]

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16 Dec 2017, 02:00
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Difficulty:

35% (medium)

Question Stats:

73% (01:42) correct 28% (01:39) wrong based on 80 sessions

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Is $$\frac{7^{(x+2)}}{49} > 1$$ ?

(1) $$7^{(x - 2)} > \frac{1}{49}$$

(2) $$7^{(x - 1)} > \frac{1}{49}$$

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Joined: 02 Aug 2009
Posts: 7967
Re: Is 7^(x + 2)/49 > 1 ?  [#permalink]

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16 Dec 2017, 06:05
Bunuel wrote:
Is $$\frac{7^{(x+2)}}{49} > 1$$ ?

(1) $$7^{(x - 2)} > \frac{1}{49}$$

(2) $$7^{(x - 1)} > \frac{1}{49}$$

Slightly tricky q..

$$\frac{7^{(x+2)}}{49} > 1..........7^x>1$$ MEANS --- Is x>0?

lets see the statements
(1) $$7^{(x - 2)} > \frac{1}{49}...........7^{(x-2+2)}>1...........7^x>1$$
Sufficient

(2) $$7^{(x - 1)} > \frac{1}{49}...........7^{(x-1+2)}>1.......7^{(x+1)}>0$$
so x+1>0....x>-1
if x is between -1 and 0 , ans is NO
otherwise Yes
insuff

A
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Is 7^(x + 2)/49 > 1 ?  [#permalink]

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16 Dec 2017, 09:10
Bunuel wrote:
Is $$\frac{7^{(x+2)}}{49} > 1$$ ?

(1) $$7^{(x - 2)} > \frac{1}{49}$$

(2) $$7^{(x - 1)} > \frac{1}{49}$$

Simplify: $$\frac{7^{(x+2)}}{49} > 1 = \frac{7^{(x+2)}}{(7^2)} > 1 =7^{(x+2)-2}> 1.$$

Question: Is $$x > 0?$$

(1) $$7^{(x - 2)} > \frac{1}{49} = 7^{(x - 2)} > \frac{1}{7^2} = 7^{(x - 2)} > 7^{(-2)} = x-2>-2 = x > 0.$$ Sufficient.

(2) $$7^{(x - 1)} > \frac{1}{49} = 7^{(x - 1)} > \frac{1}{7^2} = 7^{(x - 1)} > 7^{(-2)} = x-1>-2 = x-1+2 > 0 = x > -1.$$ Insufficient.

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Re: Is 7^(x + 2)/49 > 1 ?  [#permalink]

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23 Aug 2019, 19:17
It's mentioned in both responses that the question is asking is x>0? But what if x is a fraction, e.g. 7^1/100, still less than 1?
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Is 7^(x + 2)/49 > 1 ?  [#permalink]

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23 Aug 2019, 19:39
1
philipssonicare wrote:
It's mentioned in both responses that the question is asking is x>0? But what if x is a fraction, e.g. 7^1/100, still less than 1?

7^0 is exactly 1. So 7 raised to any power greater than 0 will always be greater than 1.

As a specific example, in the expression 7^n, as the value of the power (n) progresses from 0 to 1, the value of the expression (7^n) will progress from 1 to 7

Hope this is clear!

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Is 7^(x + 2)/49 > 1 ?   [#permalink] 23 Aug 2019, 19:39
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