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If n is a positive integer, is the value of b - a at least twice the

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NipunBagaria
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Re: If n is a positive integer, is the value of b - a at least twice the [#permalink] New post   02 Mar 2023, 07:13
Can you please put n=3 in the first statement and explain me the answer.
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Bunuel
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Re: If n is a positive integer, is the value of b - a at least twice the [#permalink] New post   02 Mar 2023, 13:04
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NipunBagaria wrote:
Can you please put n=3 in the first statement and explain me the answer.


Is the value of b - a at least twice the value of \(3^n - 2^n\) ?

If n = 3, then:

\(a= 2^{(n+1)}=16\) and \(b= 3^{(n+1)}=81\). Therefore, b - a = 65.

\(3^n - 2^n=27-8=19\).

65 is at least twice the value of 19 (65 >= 19*2).

Hope it helps.
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pchandra9695
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Re: If n is a positive integer, is the value of b - a at least twice the [#permalink] New post   24 Dec 2023, 19:59
I did reach to 3^n>=0, but how does that make the statement sufficient?

Can someone give a logical explanation without using numbers?
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Re: If n is a positive integer, is the value of b - a at least twice the [#permalink] New post   24 Dec 2023, 23:59
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pchandra9695 wrote:
I did reach to 3^n>=0, but how does that make the statement sufficient?

Can someone give a logical explanation without using numbers?


After certain algebraic manipulations, the question became (we were able to rephrase the question) "Is \(3^{n}\geq{0}\)?" A positive integer (3) in a positive integer power (n) is always positive, so the answer to this question is YES. Hence, the statement is sufficient.
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Re: If n is a positive integer, is the value of b - a at least twice the [#permalink]
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