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

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Joined: 02 Sep 2009
Posts: 46302
The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink]

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01 Aug 2017, 01:18
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:07) correct 33% (01:29) wrong based on 148 sessions

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

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01 Aug 2017, 01:53
1
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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05 Aug 2017, 09:02
1
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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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.)

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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]

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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.)

hey

???

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

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Joined: 05 Dec 2015
Posts: 4
Location: Brazil
GMAT 1: 720 Q50 V38
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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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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.)

hey

???

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

I did ctrl C and ctrl V and forgot to update the values, thanks for the reminder
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Status: love the club...
Joined: 24 Mar 2015
Posts: 275
Re: The equation n < 1/(-2)^(-n) < 135.43 is true for how many unique in [#permalink]

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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.)

hey

???

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

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

hahahaha
I got it ...

thanks
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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