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Is k^2 a prime number?

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Bunuel
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Is k^2 a prime number? [#permalink] New post   09 Jan 2017, 03:19
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Is k^2 a prime number?

(1) k is an integer.
(2) k^2 – 1 < 0
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D
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Kurtosis
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Re: Is k^2 a prime number? [#permalink] New post   09 Jan 2017, 10:12
k^2 can be prime only if k is not an integer. Ex: k = sqrt(11).

If k is an integer greater than 1, k^2 will have more than 2 factors.

St1: k is an integer. --> Sufficient. k^2 cannot be prime.

St2: k^2 – 1 < 0 --> k^2 < 1 --> Sufficient. k^2 cannot be prime.

Answer: D
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Re: Is k^2 a prime number? [#permalink] New post   10 Jan 2017, 04:34
Bunuel wrote:
Is k^2 a prime number?

(1) k is an integer.
(2) k^2 – 1 < 0



Statement 1: k is an integer

K= 0 ... k^2=0 Not prime

K=2 .....k^2=1 Not prime

K=2 or 3 oe any number means k^2 won't be prime.

Sufficient

k^2 – 1 < 0...... k^2 < 1....... -1<k< 1.......it means k is fraction.......K not prime

Sufficient

Answer: D
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Re: Is k^2 a prime number? [#permalink] New post   10 Jan 2017, 07:07
Nice one.
Here is what i did in this one =>
We ned to see if k is prime or not.
Statement 1=> k is an integer => k^2 can never be an integer.
Sufficient
Statement 2=> k^2<1
=> k must lie in the range => (-1,1)
So k can never be prime.
Hence sufficient.
Hence D.
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Re: Is k^2 a prime number? [#permalink] New post   10 Jan 2017, 07:14
1. if k is an integer, then k^2 definitely is not a prime number.
2. k^2 -1 < 0 -> k^2 < 1. k^2 is definitely not a prime number.

answer is D.
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Re: Is k^2 a prime number? [#permalink] New post   11 Jan 2017, 07:52
Expert Reply
Bunuel wrote:
Is k^2 a prime number?

(1) k is an integer.
(2) k^2 – 1 < 0


We need to determine whether k^2 is a prime number.

Statement One Alone:

k is an integer.

Since k is an integer, there is no value for k that will allow k^2 to be prime. Thus, k^2 IS NOT a prime number. Statement one alone is sufficient to answer the question.

Statement Two Alone:

k^2 – 1 < 0

We can simplify the inequality:

k^2 – 1 < 0

k^2 < 1

Since k^2 must be positive, 0 < k^2 < 1, so k^2 is a positive proper fraction and thus cannot be prime. Statement two is also sufficient to answer the question.

Answer: D
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Re: Is k^2 a prime number? [#permalink] New post   09 Jul 2019, 09:16
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Re: Is k^2 a prime number? [#permalink]
09 Jul 2019, 09:16
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