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

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Math Expert
Joined: 02 Sep 2009
Posts: 58469
If k is a positive integer, what is the value of k?  [#permalink]

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26 Feb 2018, 03:15
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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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26 Feb 2018, 03:22
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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26 Feb 2018, 03:24
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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If k is a positive integer, what is the value of k?  [#permalink]

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26 Feb 2018, 03:26
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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26 Feb 2018, 04:41
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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

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

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26 Feb 2018, 05:36
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.

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.

Sufficient

really good question as always by Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 58469
Re: If k is a positive integer, what is the value of k?  [#permalink]

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24 Dec 2018, 02:43
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.

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Re: If k is a positive integer, what is the value of k?   [#permalink] 24 Dec 2018, 02:43
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