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If n is a prime number, which of the following could be true?

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janosfazekas91
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If n is a prime number, which of the following could be true? [#permalink] New post   Updated on: 02 Aug 2021, 11:18
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If n is a prime number, which of the following could be true?


A. \(n^n=n\)

B. \(\frac{n^2}{4}\) is even

C. \((n)(n^n)\) is negative

D. \(n^2+n^3= n^5\)

E. \(\frac{n^n}{4} = 1^{(n-1)}\)
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E

Originally posted by janosfazekas91 on 13 Mar 2015, 03:58.
Last edited by Bunuel on 02 Aug 2021, 11:18, edited 2 times in total.
Renamed the topic and edited the question.
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thefibonacci
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   13 Mar 2015, 04:07
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janosfazekas91 wrote:
Hey guys,

I have encountered the following problem, can somebody please explain how you get qucikly to the answer?

If n is a prime number, which of the following could be true?

n^n=n

n^2/4= is even

(n)(n^n) = is negative

n^2+n^3= n^5

n^n/4 = 1^(n-1)

Thanks


E should be the answer.

2^2/4 = 1^(2-1)
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chetan2u
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   13 Mar 2015, 06:12
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if n is a prime number
1)n^n=n
2)n^2/4= is even
3)(n)(n^n) = is negative
4)n^2+n^3= n^5
5)n^n/4 = 1^(n-1)....

hi the easiest and fastest method to do is knowing that only one prime number is even and rest odd and fixing this on the choices..
1)n^n=n
no integer except 1 can fit in so out

2)n^2/4= is even
we know only 2 is even prime number and n^2/4 is one... so out
3)(n)(n^n) = is negative
all values are positive so cannot be true...
4)n^2+n^3= n^5
this is not possible as n^2*n^3= n^5
5)n^n/4 = 1^(n-1)
n as 2 straight way gives the answer....
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   13 Mar 2015, 06:20
Expert Reply
chetan2u wrote:
1)n^n=n
no integer except 0 and 1 can fit in so out


0 does not fit.

0^0 is undefined and not tested on the GMAT.
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ak1802
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   14 Mar 2015, 08:22
There are two sets of "n" prime numbers you should be concerned with here while testing solutions:

- 2
- all other prime numbers

This will help you arrive at the answer that much faster.

Posted from my mobile device
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   03 Feb 2016, 19:05
janosfazekas91 wrote:
If n is a prime number, which of the following could be true?

A. n^n=n
B. n^2/4= is even
C. (n)(n^n) = is negative
D. n^2+n^3= n^5
E. n^n/4 = 1^(n-1)


right away, we can eliminate C - prime number multiplied by another prime number raised to itself - can never be negative.
n^n=n only when n=1. thus, it can't be. A is out.
B - never true. if n=2, then it's odd. if n is any other prime number, then the result is a non-integer.
D - try with the lowest possible prime numbers: 2^2+2^3 = 4+8=12. can't be expressed as n^5. with n=3 the same..the more we try, the more we realize it's impossible.
E however, works fine. if n=2, then 2^2/4 = 1. and 1^(2-1) = 1. which is true.

so E it is possible.
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   23 Aug 2016, 06:47
Excellent Question
Teaches us quite a few concepts
Here we need to check each option individually
Clearly if n=2 => E is correct
Smash that E
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   22 Sep 2017, 01:05
janosfazekas91 wrote:
If n is a prime number, which of the following could be true?

A. n^n=n
B. n^2/4= is even
C. (n)(n^n) = is negative
D. n^2+n^3= n^5
E. n^n/4 = 1^(n-1)


A. n^n = n
n(n^(n-1) - 1)
So, n =1 is only possible value.

B. if we put value, 2 then 2^2/4 = 1 is odd. In other cases n^2/4 has decimal value.

C. n(n^n) can never be -ve for prime numbers

D. n^2 + n^3 = n^5
n^2 (n^3-n+1) = 0
No such prime number exists

E. For n =2 , n^n/4 = 1^(n-1) is true.

So, Answer E
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skhemani
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   13 Jan 2019, 03:48
Could any one please explain the answer... Considering n=2 here,
n^n/4 = 2^2/4 = 2^1/2
How does this equal 1? Are we taking and approximation here?
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   18 Jan 2019, 06:04
skhemani wrote:
Could any one please explain the answer... Considering n=2 here,
n^n/4 = 2^2/4 = 2^1/2
How does this equal 1? Are we taking and approximation here?


skhemani
I have the same question. I think the problem expects us to round sq. root of 2, i.e 1.414 to 1.

That's the only way I see E as the correct answer.

May be we can take some hint from *could be* true (and not must be true).

Here the "could be" scenario is "could be true if approximation is performed on LHS."

Hope my understanding is correct.

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Re: If n is a prime number, which of the following could be true? [#permalink] New post   12 Mar 2019, 12:32
Actually, the last option E is 2*2/4 = 4/4 =1 and not 2 raised to power 2/4.
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   02 Aug 2021, 11:04
janosfazekas91 wrote:
If n is a prime number, which of the following could be true?

A. n^n=n
B. n^2/4= is even
C. (n)(n^n) = is negative
D. n^2+n^3= n^5
E. n^n/4 = 1^(n-1)


Can someone put parenthesis on this question? I read it as n^(n/4) thanks!
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   02 Aug 2021, 11:23
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kelbyandrews wrote:
janosfazekas91 wrote:
If n is a prime number, which of the following could be true?

A. n^n=n
B. n^2/4= is even
C. (n)(n^n) = is negative
D. n^2+n^3= n^5
E. n^n/4 = 1^(n-1)


Can someone put parenthesis on this question? I read it as n^(n/4) thanks!


n^n/4 can only mean \(\frac{n^n}{4}\). If it were \(n^{\frac{n}{4}}\) it would have been written as n^(n/4). Still edited. Thank you for the suggestion.
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kelbyandrews
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Re: If n is a prime number, which of the following could be true? [#permalink] New post   02 Aug 2021, 11:29
Ahh that makes sense. Thank you for editing though!

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Re: If n is a prime number, which of the following could be true? [#permalink]
02 Aug 2021, 11:29
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