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

Question

(1) k < 10

(2) k < 5

Chethan92 · Answer

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.

PKN · Answer

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.

chetan2u · Answer

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

PKN · Answer

Thank you Sir, I am happy that my understanding is correct. i was biased a bit.

I will keep my post as it is.

hasnain3047 · Answer

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

PKN · Answer

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

ocelot22 · Answer

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

gvij2017 · Answer

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.

BrentGMATPrepNow · Answer

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

Answer: E

Cheers,
Brent

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

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

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