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

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Bunuel
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The equation n < 1/{(-2)^{-n}} < 135.43 is true for how many [#permalink] New post   01 Oct 2017, 22:20
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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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Re: The equation n < 1/{(-2)^{-n}} < 135.43 is true for how many [#permalink] New post   02 Oct 2017, 00:07
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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

Kudos for correct solution.



we can rephrase the statement as

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

Given n is prime number, and it should also be an even number to satisfy the equation

SO there is only one option for n i.e 2 (since it is even and prime number)

Hence ans is D.
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Re: The equation n < 1/{(-2)^{-n < 135.43 is true for how many [#permalink] New post   01 Sep 2024, 01:18
Why do you say it should be positive? there is nothing in the question that implies. Correct me if I'm wrong. Integer can be negative too, that's why there are infinite solutions.
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Re: The equation n < 1/{(-2)^{-n < 135.43 is true for how many [#permalink] New post   09 Oct 2024, 08:22
Can you please share a more elaborate explanation for this one? Why are we assuming that n has to be even?
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The equation n < 1/{(-2)^{-n < 135.43 is true for how many [#permalink] New post   09 Oct 2024, 08:50
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here the logic is that, according to the rules of exponents, we can write the stem in the following way

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

Now

we do know that n is prime and we have ONLY one prime even and all the others infinite prime are odd. The prime numbers are only positive

To have -2^n between n and 135.43 n must be 2- If we use 3 then we do have that

\(3<-8<135.43\) which han NO SENSE

If we use 2 we have

\(2<4<135.43\)

Therefore, n can have ONLY one possible value: the 2

I hope now is clear
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The equation n < 1/{(-2)^{-n < 135.43 is true for how many [#permalink]
09 Oct 2024, 08:50
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