If k is a positive integer, is k an integer?

Question

If k is a positive integer, is  \sqrt{k}  an integer?

(1) k is even.
(2) k =  \sqrt{m} , where m is an integer.

gmatser1 · Answer

I understand how (1) and (2) is not sufficient, but I don't get how they are not sufficient together. If k is even and k is the square root of m, shouldn't that mean that the square root of k is never an integer since 2 will be in k?

IanStewart · Answer

When you take the square root of an even number, sometimes you get an integer, sometimes not - √2 is not an integer, but √4 is an integer. So S1 is not sufficient.

Every positive integer is the square root of some other integer (2 is the square root of 4, 3 is the square root of 9, etc) so Statement 2 tells us nothing whatsoever, and since S1 is not sufficient, the answer must be E.

Harley1980 · Answer

Hello  gmatser1 
m can be equal to 16 and then k = 4 -> integer

EMPOWERgmatRichC · Answer

Hi gmatser1,

This question can be solved rather quickly by TESTing VALUES.

We're told that K is a POSITIVE INTEGER. We're asked if √K is an integer. This is a YES/NO question.

Fact 1: K is EVEN

IF....
K = 2
√2 is NOT an integer, so the answer to the question is NO

IF...
K = 4
√4 = 2 and that IS an integer, so the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: K =√M where M is an INTEGER

IF....
K = 2, M = 4
√2 is NOT an integer, so the answer to the question is NO

IF...
K = 4, M = 16
√4 = 2 and that IS an integer, so the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we don't need to do any additional work. We already have 2 possibilities that fit BOTH Facts (one gives us a NO answer and one gives us a YES answer).
Combined, INSUFFICIENT

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

ujwalsn · Answer

m can be equal to 16 and then k = 4 -> integer

Divyadisha · Answer

(1) k is even. 
k can be 2, 4, 6, 8, 10.... and hence  \sqrt{k}  may or may not be an integer.

(2) k =  \sqrt{m} , where m is an integer.

K can be 1, 2, 3, 4, .... and hence  \sqrt{k}  may or may not be integer

combining both statements

k can be 2, 4... and hence  \sqrt{k}  may or may not be an integer.

Both statements together are insufficient. E is the answer

MHIKER · Answer

1) 2 is even and the root of 2 is not an integer.
2) Same; k= root of 4 which will be an integer. Here also we will get 2; and root of 2 will not be an integer.

Trying both;
We can use the same explanation. 
2 is even and root of 4, which could be result of root of m.

so answer is E.

If k is a positive integer, is k an integer?

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GMAT Data Sufficiency (DS) Questions

If k is a positive integer, is k an integer?

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