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Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2

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Bunuel
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Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   20 Oct 2014, 06:59
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Is \(5^n < 0.04\)?


(1) \((\frac{1}{5})^n > 25\)

(2) \(n^3 < n^2\)
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A
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Bunuel
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Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   16 Mar 2015, 08:59
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Is \(5^n < 0.04\)?


Is \(5^n < 0.04\)?

Is \(5^n < \frac{1}{25}\) ?

Is \(5^n < \frac{1}{5^2}\) ?

Is \(5^n < 5^{(-2)}\)?

Is \(n < -2\)?


(1) \((\frac{1}{5})^n > 25\) --> \(\frac{1}{5^n} > 25\) --> \(5^n < \frac{1}{25}\) --> \(5^n < 0.04\). Sufficient.

(2) \(n^3 < n^2\) --> \(n < 0\) or \(0 < n < 1\). Not sufficient.


Answer: A.
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   20 Oct 2014, 22:15
Is 5^n < 0.04?

(1) (1/5)^n > 25
(2) n^3 < n^2[/quote]

Notice that for \(n\geq{0}\) so RHS of the Q stem is always greater than zero so we need to confirm whether n<-2 because\(5^{-2}\) is 1/25 =0.04

St 1 says (1/5)^n > 25 or n>2 so st 1 is sufficient as n is positive

St 2 says n^3<n^2 or n(n^2-1)<0 or n(n-1)(n+1) <0
Key points are n=0,-1 and 1

So we have 4 range

Case 1: n<-1 The expression n(n-1)(n+1) <0 is true
Case 2: -1<n<0, The expression is is false as it will be >0
Case3 : 0<n<1, The expression will be true
and Case 4: n>1 The expression will be true for all values

Since, we have 2 ranges in which expression holds true and for those range n <-2 or n>-2..

Ans is A
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   Updated on: 16 Mar 2015, 10:18
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study4job wrote:
Is 5^n < 0.04?

(1) (1/5)^n > 25

(2) n^3 < n^2



Given \(5^n < 0.04\)
\(5^n < 0.04 ( 0.04=4/100=1/25=5^{-2 }\)
\(n<-2 ?\)

option A:
\(5^{- n} > 25=5^2\) ; implies n<-2 SUFFICIENT
option B:

\(n^3 < n^2 \\
==> n^3-n^2 <0 \\
==> n^2(n-1) <0 \\
==> n-1<0 \\
==> n<1\) NOT SUFFICIENT.

Bunuel , have i solved the second inequality incorrectly ?

thanks
lucky

Originally posted by Lucky2783 on 16 Mar 2015, 10:05.
Last edited by Lucky2783 on 16 Mar 2015, 10:18, edited 2 times in total.
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   16 Mar 2015, 10:17
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Lucky2783 wrote:
study4job wrote:
Is 5^n < 0.04?

(1) (1/5)^n > 25

(2) n^3 < n^2



Given \(5^n < 0.04\)
\(5^n < 0.04 ( 0.04=4/100=1/25=5^{-2 }\)
\(n<-2 ?\)

option A:
\(5^{- n} > 25=5^2\) ; implies n<-2 SUFFICIENT
option B:

n^3 < n^2
==> n^3-n^2 <0
==> n^2(n-1) <0
==> n-1<0
==> n<1 NOT SUFFICIENT.


Small correction: for (2) it should be n < 0 or 0 < n < 1. 0 must be excluded, because for n = 0, n^3 < n^2 does not hold true.
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   16 Mar 2015, 10:20
Bunuel wrote:
Lucky2783 wrote:
study4job wrote:
Is 5^n < 0.04?

(1) (1/5)^n > 25

(2) n^3 < n^2



Given \(5^n < 0.04\)
\(5^n < 0.04 ( 0.04=4/100=1/25=5^{-2 }\)
\(n<-2 ?\)

option A:
\(5^{- n} > 25=5^2\) ; implies n<-2 SUFFICIENT
option B:

n^3 < n^2
==> n^3-n^2 <0
==> n^2(n-1) <0
==> n-1<0
==> n<1 NOT SUFFICIENT.


Small correction: for (2) it should be n < 0 or 0 < n < 1. 0 must be excluded, because for n = 0, n^3 < n^2 does not hold true.



got it Bunuel . i missed it. thanks so much .
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   29 Aug 2015, 05:12
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Here is my approach:

Statement 1:
\(\frac{1}{5}^n > 25\)
\(5^-n > 5^2\)
\(-n > 2\)
\(n < -2\)

plug in n=-3 into the equation will yield that 1/125 is < than 0,04

Sufficient

Statement 2:
per statement n can be either a negative number or a proper fraction. 5^(1/2) would be > 0,04 while to a negative power would be <. not sufficient.

--> A
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   27 Jan 2019, 07:35
Bunuel wrote:

Tough and Tricky questions: Absolute Values.



Is 5^n < 0.04?

(1) (1/5)^n > 25
(2) n^3 < n^2



Hi gmatbusters, Can you please share your thoughts on inline approach.

Is this a validate approach ??

is 5^n < 5^-2
becomes is n < -2 ??

1) 5^(-n) > 5^2
=> -n > 2
=> n < -2
Sufficient

2) Can't tell anything from this.
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   27 Jan 2019, 19:49
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Hii

Your approach to use first statement is correct.

For second statement.
n^3 < n^2
n^2(n-1)<0
n < 1
But since now n can be < or > -2, statement 2 is not sufficient

Hence Answer - A

KanishkM wrote:
Bunuel wrote:

Tough and Tricky questions: Absolute Values.



Is 5^n < 0.04?

(1) (1/5)^n > 25
(2) n^3 < n^2



Hi gmatbusters, Can you please share your thoughts on inline approach.

Is this a validate approach ??

is 5^n < 5^-2
becomes is n < -2 ??

1) 5^(-n) > 5^2
=> -n > 2
=> n < -2
Sufficient

2) Can't tell anything from this.
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   04 Apr 2019, 03:32
Bunuel wrote:

Tough and Tricky questions: Absolute Values.



Is 5^n < 0.04?

(1) (1/5)^n > 25
(2) n^3 < n^2


Question : Is \(5^n < 0.04\) ?

Or Is \(5^n < \frac{4}{100}\) ?

Or Is \(5^n < 5^{-2}\) ?

Finally, Is \(n < -2\) ?

Statement 1 : \(\frac{{1^n}}{{5}^n} > 25\)

Or 5\(^{-n} > 5^2\)

Or \(-n > 2\)

Or \(n < -2\) (Answer to the question, YES) SUFFICIENT

Statement 2 :

\(n^3 < n^2\) (As \(n^2\) will always be positive, divide both sides by n^2)

We get, n < 1

If \(n = 0\), the answer to the question is NO

If \(n = - 3\), the answer to the question is YES

NOT SUFFICIENT
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   15 Jan 2021, 22:40
Pretty tricky.

Is 5^n < 0.04?

(1) (1/5)^n > 25
(2) n^3 < n^2

The question is asking 5^n < 0.04? This is the same as 5^n < 5^-2? In other words, is n less than -2?

(1) (1/5)^n > 25 ----> 5^-n > 5^2 ---> -n > 2 ---> n < -2
Sufficient.

(2) n^3 < n^2
n^3 - n^2 < 0
n^2 (n - 1) < 0 ---> Implies that n is negative, but n can be -1, -2, -3...Each of these satisfies the inequality.
Insufficient.
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink] New post   04 Jun 2023, 12:32
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Re: Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 [#permalink]
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