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If k is a positive integer, what is the value of k?

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If k is a positive integer, what is the value of k?  [#permalink]

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New post 26 Feb 2018, 02:15
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GMAT CLUB'S FRESH QUESTION.



If k is a positive integer, what is the value of k?


(1) \(\sqrt{2k}\) is the greatest factor of k.

(2) \(\frac{k}{2}\) is the smallest factor of k.

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Re: If k is a positive integer, what is the value of k?  [#permalink]

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New post 26 Feb 2018, 02:22
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION.



If k is a positive integer, what is the value of k?


(1) \(\sqrt{2k}\) is the greatest factor of k.

(2) \(\frac{k}{2}\) is the smallest factor of k.


a) rt 2k is the greatest factor of k

i.e rt2k= k
squaring

2k=k^2
k=2

sufficient

b) k/2 is the smallest factor of k

let k =4

4/2 = 2

but smallest factor is 1
so k/2 can't be greater than 1

k/2=1
k=2

sufficient

(D) imo
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Re: If k is a positive integer, what is the value of k?  [#permalink]

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New post 26 Feb 2018, 02:24
Hatakekakashi wrote:
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION.



If k is a positive integer, what is the value of k?


(1) \(\sqrt{2k}\) is the greatest factor of k.

(2) \(\frac{k}{2}\) is the smallest factor of k.


a) rt 2k is the greatest factor of k

i.e rt2k= k

squaring

2k=k^2
k=2

sufficient

b) k/2 is the smallest factor of k

let k =4

4/2 = 2

but smallest factor is 1
so k/2 can't be greater than 1

k/2=1
k=2

sufficient

(D) imo


Writing Mathematical Formulas on the Forum: https://gmatclub.com/forum/rules-for-po ... l#p1096628
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Collection of Questions:
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If k is a positive integer, what is the value of k?  [#permalink]

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New post 26 Feb 2018, 02:26
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION.



If k is a positive integer, what is the value of k?


(1) \(\sqrt{2k}\) is the greatest factor of k.

(2) \(\frac{k}{2}\) is the smallest factor of k.


1. K is a positive integer
2. we are looking for the value of K

statement 1: \sqrt{2k} is a factor of K . in order to make it an integer k has to be 2. here \sqrt{2k} is the greatest factor.
statement 2: smallest factor for any integers is 1. k/2 is the smallest integer. K must be 2 in order to obtain 1.

both of the statements are sufficient. Answer D.
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Re: If k is a positive integer, what is the value of k?  [#permalink]

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New post 26 Feb 2018, 03:41
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION.



If k is a positive integer, what is the value of k?


(1) \(\sqrt{2k}\) is the greatest factor of k.

(2) \(\frac{k}{2}\) is the smallest factor of k.


Given : k is a positive Integer

Question : Value of k = ?

Statement 1: \(\sqrt{2k}\) is the greatest factor of k.
since the factor of any positive integer is essentially an Integer hence
\(\sqrt{2k}\) must be n integer

Also, the Greatest factor of any positive Integer is the same Number itself

hence, \(\sqrt{2k}\) = k
Squaring both sides we get

\(k^2 = 2k\)
i.e. k = 0 or 2

but since we already know that k is a positive Integer hence, k = 2

SUFFICIENT


Statement 2: \(\frac{k}{2}\) is the smallest factor of k.

The smallest factor of any positive Integer is 1 hence

k/2 = 1

and k = 2

SUFFICIENT

Answer: Option D
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Re: If k is a positive integer, what is the value of k?  [#permalink]

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New post 26 Feb 2018, 04:36
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION.



If k is a positive integer, what is the value of k?


(1) \(\sqrt{2k}\) is the greatest factor of k.

(2) \(\frac{k}{2}\) is the smallest factor of k.


Let's plug in some values

Statement 1

Let k = 2..........\(\sqrt{4}\)= 2, which is the greatest factor of k.

Let k = 8...........\(\sqrt{16}\)= 4, which is NOT the greatest factor of k.

Let k =18...........\(\sqrt{36}\)= 6, which is NOT the greatest factor of k.

Let k =50...........\(\sqrt{100}\)= 10, which is NOT the greatest factor of k.

One Certain answer...k=2

Sufficient

Statement 2

Let k = 2..........\(\frac{2}{2}\)= 1, which is the smallest factor of k.

Let k = 8...........\(\frac{8}{2}\)= 4, which is NOT the smallest factor of k.

Let k =18...........\(\frac{18}{2}\)= 9, which is NOT the smallest factor of k.

Let k =50...........\(\frac{50}{2}\)= 25, which is NOT the smallest factor of k.

One Certain answer...k=2

Sufficient

Answer: D

really good question as always by Bunuel :-)
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Re: If k is a positive integer, what is the value of k? &nbs [#permalink] 26 Feb 2018, 04:36
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If k is a positive integer, what is the value of k?

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