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

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

(1) k < 10

(2) k < 5

HIGH QUALITY QUESTION!!!!

This is exactly the kind of question that reading too quickly will punish you for. rootk is not an integer. is root k prime? My mind immediately goes to think k is an integer" cause why would someone ask if something off the wall like k=2.5 is prime?" the problem doesnt say that k is an integer. Get in the habit of immediately writing on your pad K=ANYTHING

(1) k<10 k = 5, yes, k=2.5 no
NS
(2) K <5 k =2 yes , k=2.5 no ns

(1) and (2) k<10 and K<5 means simply k<5. K=2 yes. k=2.5 no NS

OA is E
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Re: If √k is not an integer, then is k a prime number? [#permalink]
Answer E is correct but K can't be negative as square root of negative value is imaginary number which is not in scope of GMAT.

Question stem tell that K>0 at first glance.
Now hope you have your clarification.

PKN wrote:
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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Re: If √k is not an integer, then is k a prime number? [#permalink]
1
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Top Contributor
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

Target question: Is k a prime number?

Statement 1: k < 10
Let's TEST some values.
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, k is NOT a prime number
Case b: k = 3 (√3 is not an integer). In this case, the answer to the target question is YES, k IS a prime number
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k < 5
Let's TEST some values.
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, k is NOT a prime number
Case b: k = 3 (√3 is not an integer). In this case, the answer to the target question is YES, k IS a prime number
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, k is NOT a prime number
Case b: k = 3 (√3 is not an integer). In this case, the answer to the target question is YES, k IS a prime number
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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