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# If √k is not an integer, then is k a prime number?

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Math Expert
Joined: 02 Sep 2009
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If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 02:52
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Difficulty:

55% (hard)

Question Stats:

45% (00:52) correct 55% (00:42) wrong based on 67 sessions

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If √k is not an integer, then is k a prime number?

(1) k < 10

(2) k < 5

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Joined: 18 Jul 2018
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Concentration: Finance, Marketing
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Re: If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 03:05
1
From statement 1: If we take K as 8 then $$\sqrt{k}$$ = 2$$\sqrt{2}$$. Not an integer. But, 8 is not prime. If we take 7 then $$\sqrt{k}$$ is not an integer. But k is prime. Hence 1 is Insufficient.
From statement 2: If we take K as 2, 3 or 5. $$\sqrt{k}$$ is not an integer. And all the values of K are prime. Hence, B is sufficient.
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Re: If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 05:58
Bunuel wrote:
If √k is not an integer, then is k a prime number?

(1) k < 10

(2) k < 5

Given, √k is not an integer, implies k is not a perfect square.

Question stem:- Is k a prime number?

St1:- k < 10

Possible values of k:- 1,2,3,4,5,6,7,8,9

k: 2,3,5,7 --> Prime
k: 6,8-----> Not prime.
Insufficient.

St2:- k < 5
Possible values of k:- 1,2,3,4
k: 2,3----> Prime
Sufficient.

Ans. (B)

P.S:- Here it is given that √k is not an integer. k is not necessarily an integer, it could be a positive rational number too.
In st2, k<5. Possible values of k could be any number between 0 to 5.

If I say k=0.5, √k is not an integer. hence, k is also not a prime number.

chetan2u, could you please clear my confusion. I know, an integer can be prime. I think it would be clear if the question stem mentions k to be an integer.
Expert comment please.
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Re: If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 06:11
Bunuel wrote:
If √k is not an integer, then is k a prime number?

(1) k < 10

(2) k < 5

Hi PKN

We have to read the question as it is and therefore answer should be E..

Since k can be 1.4, then it is NOT prime
If k is 3, it is Prime..
So insufficient

Answer would be B if it was given as an integer but that may be the catch
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 06:15
chetan2u wrote:
Bunuel wrote:
If √k is not an integer, then is k a prime number?

(1) k < 10

(2) k < 5

Hi PKN

We have to read the question as it is and therefore answer should be E..

Since k can be 1.4, then it is NOT prime
If k is 3, it is Prime..
So insufficient

Answer would be B if it was given as an integer but that may be the catch

Thank you Sir,
I am happy that my understanding is correct. i was biased a bit.
I will keep my post as it is.
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PKN

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Re: If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 08:41
can 'k' take negative values as its not mentioned in the statement whether its positive or negative?
in that case answer would be 'E'.
k can also take fractional values so 'E' would be answer in that case as well
plz clarify
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Hasnain Afzal

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Re: If √k is not an integer, then is k a prime number?  [#permalink]

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13 Aug 2018, 09:16
hasnain3047 wrote:
can 'k' take negative values as its not mentioned in the statement whether its positive or negative?
in that case answer would be 'E'.
k can also take fractional values so 'E' would be answer in that case as well
plz clarify

Yes. You are absolutely correct. E must be the answer.
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PKN

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Re: If √k is not an integer, then is k a prime number? &nbs [#permalink] 13 Aug 2018, 09:16
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# If √k is not an integer, then is k a prime number?

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