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

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

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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
[Reveal] Spoiler: OA

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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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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
D
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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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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]

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New post 05 Aug 2017, 17:37
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.
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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]

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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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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink]

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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]

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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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Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in   [#permalink] 08 Aug 2017, 09:59
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