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The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in

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Bunuel
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The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   01 Aug 2017, 01:18
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The equation \(n < \frac{1}{{(-2)^{-n}}} < 135.43\) is true for how many unique integer values of n, where n is a prime number?

A. 7
B. 4
C. 2
D. 1
E. 0
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D
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Luckisnoexcuse
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   01 Aug 2017, 01:53
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Bunuel wrote:
The equation \(n < \frac{1}{{(-2)^{-n}}} < 135.43\) is true for how many unique integer values of n, where n is a prime number?

A. 7
B. 4
C. 2
D. 1
E. 0


\(n < \frac{1}{{(-2)^{-n}}} < 135.43\)
n has to be + as NO negative numbers are prime nos. Hence (-2)^n should also be positive
only even values of n can yield positive result
Only even prime number is 2. Hence n can take only 1 value i.e. 2
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   05 Aug 2017, 09:02
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Bunuel wrote:
The equation \(n < \frac{1}{{(-2)^{-n}}} < 135.43\) is true for how many unique integer values of n, where n is a prime number?

A. 7
B. 4
C. 2
D. 1
E. 0


\(n < \frac{1}{{(-2)^{-n}}} < 135.43\)

n < (-2)^n < 135.43

Since n is a prime number, by putting numbers-
n=2, 2< 4< 135.43
For n=3,5,7 the equation doesn't hold

So, ans is D) 1.
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The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   Updated on: 08 Aug 2017, 07:37
The expression n < 1/(-2)^(-n) < 135.43 is equivalent to n < \((-2)^{n}\) < 135.43

For n=2: 2 < 4 < 135.43 OK
For n=3: 3 < -27 < 135.43 NOT OK
For n=5: 5 < -32 < 135.43 NOT OK
For n=7: 7 < -128 < 135.43 NOT OK

Since 2 is the only even prime number, we didn't even have to test the other cases (n=3,5,7, etc.)

Correct answer is D.

Originally posted by lukera on 05 Aug 2017, 17:37.
Last edited by lukera on 08 Aug 2017, 07:37, edited 2 times in total.
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   08 Aug 2017, 03:44
lukera wrote:
The expression n < 1/(-2)^(-n) < 135.43 is equivalent to n < \((-2)^{n}\) < 135.43

For n=2: 2 < 4 < 135.43 OK
For n=3: 2 < -27 < 135.43 NOT OK
For n=5: 2 < -32 < 135.43 NOT OK
For n=7: 2 < -128 < 135.43 NOT OK

Since 2 is the only even prime number, we didn't even have to test the other cases (n=3,4,5, etc.)

Correct answer is D.



hey

???

you have plugged prime values such as 3,5 , and 7, but you didn't put the values in place of "n" ...
why....?

thanks in advance ..
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lukera
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   08 Aug 2017, 07:38
ssislam wrote:
lukera wrote:
The expression n < 1/(-2)^(-n) < 135.43 is equivalent to n < \((-2)^{n}\) < 135.43

For n=2: 2 < 4 < 135.43 OK
For n=3: 2 < -27 < 135.43 NOT OK
For n=5: 2 < -32 < 135.43 NOT OK
For n=7: 2 < -128 < 135.43 NOT OK

Since 2 is the only even prime number, we didn't even have to test the other cases (n=3,4,5, etc.)

Correct answer is D.



hey

???

you have plugged prime values such as 3,5 , and 7, but you didn't put the values in place of "n" ...
why....?

thanks in advance ..



I did ctrl C and ctrl V and forgot to update the values, thanks for the reminder :-D
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   08 Aug 2017, 09:59
lukera wrote:
ssislam wrote:
lukera wrote:
The expression n < 1/(-2)^(-n) < 135.43 is equivalent to n < \((-2)^{n}\) < 135.43

For n=2: 2 < 4 < 135.43 OK
For n=3: 2 < -27 < 135.43 NOT OK
For n=5: 2 < -32 < 135.43 NOT OK
For n=7: 2 < -128 < 135.43 NOT OK

Since 2 is the only even prime number, we didn't even have to test the other cases (n=3,4,5, etc.)

Correct answer is D.



hey

???

you have plugged prime values such as 3,5 , and 7, but you didn't put the values in place of "n" ...
why....?

thanks in advance ..



I did ctrl C and ctrl V and forgot to update the values, thanks for the reminder :-D


hahahaha
I got it ...

thanks :lol:
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DaniyalAlwani
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   21 May 2020, 15:03
shoumkrish

Answer should be c then? because that's 2..

Am I missing something?
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   15 Jun 2020, 08:04
DaniyalAlwani wrote:
shoumkrish

Answer should be c then? because that's 2..

Am I missing something?


Hey, the question asks for how MANY integral values.. hence the answer is "for ONE value" therefore "1" is the correct answer. if it had asked for which integer then the answer would've been 2.
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink] New post   28 Apr 2023, 06:37
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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink]
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