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# Is [5^(x+2)] / 25 < 1?

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Manager
Joined: 30 May 2008
Posts: 53
Is [5^(x+2)] / 25 < 1?  [#permalink]

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14 Apr 2012, 00:29
2
11
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:06) correct 20% (01:25) wrong based on 380 sessions

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Is [5^(x+2)] / 25 < 1?

(1) 5^x <1
(2) x < 0

Can someone please check my solution see if it can be done this way?

Simplify question stam [5^(x+2)] / 25 < 1
=> [5^(x+2)] / 5^2 < 1
=> 5^(x+2) < 5^2
=> x+2 < 2
=> x<0 (so statement 2 is true)

For statement 1, the only way that 5^x < 1 is if x is negative, thus 1/(5^x) < 1

Math Expert
Joined: 02 Sep 2009
Posts: 51067
Re: Is [5^(x+2)] / 25 < 1?  [#permalink]

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14 Apr 2012, 00:40
1
2
catty2004 wrote:
Is [5^(x+2)] / 25 < 1?

(1) 5^x <1
(2) x < 0

Can someone please check my solution see if it can be done this way?

Simplify question stam [5^(x+2)] / 25 < 1
=> [5^(x+2)] / 5^2 < 1
=> 5^(x+2) < 5^2
=> x+2 < 2
=> x<0 (so statement 2 is true)

For statement 1, the only way that 5^x < 1 is if x is negative, thus 1/(5^x) < 1

Is $$\frac{5^{x+2}}{25} < 1$$?

Is $$\frac{5^{x+2}}{25} < 1$$? --> is $$\frac{5^{x+2}}{5^2} < 1$$? --> is $$5^{x+2-2}< 1$$? Finally the question becomes: is $$5^x<1$$? or is $$x<0$$?

(1) 5^x <1 --> directly answers the question. Sufficient.
(2) x < 0 --> directly answers the question. Sufficient.

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Intern
Joined: 18 Jan 2017
Posts: 36
Re: Is [5^(x+2)] / 25 < 1?  [#permalink]

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18 Jan 2017, 21:29

(2) x < 0

[5^(x+2)] / 25 = 5^x

For any value of x < 0, 5^x will always be < 1.

This is because even if x is a very small value between -1 and 0 (let us say -0.0000001), then 5^(-0.0000001) = 1/5^0.0000001

5^0.0000001 will always be > 1. Hence, 1/5^0.0000001 will always be < 1.

My question is: How do we know that 5^0.0000001 will always be > 1?
Manager
Joined: 25 Mar 2013
Posts: 242
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: Is [5^(x+2)] / 25 < 1?  [#permalink]

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23 Jan 2017, 11:25
Solve equation
5^x+2-2 < 1
5^x < 1
1,5^x < 1
2, x < 0
x = -1
$$5^{-1}$$ < 1
$$\frac{1}{5}$$ < 1
D
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Re: Is [5^(x+2)] / 25 < 1?  [#permalink]

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10 Jul 2018, 09:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is [5^(x+2)] / 25 < 1? &nbs [#permalink] 10 Jul 2018, 09:10
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