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

Question

GMAT CLUB'S FRESH QUESTION.

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

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

M36-97

Bunuel · Accepted Answer

Official Solution:

If  k  is a positive integer, what is the value of  k ? 
 
(1)  \sqrt{2k}  is the greatest factor of  k .
 
The greatest factor of a positive integer is the integer itself. So, we are given that  \sqrt{2k}=k ; 
 
Square:  2k=k^2 ;
 
 k(2-k)=0 ;
 
 k=0  (discard because we are given that  k  is a positive integer) or  k=2 . Sufficient.
 
(2)  \frac{k}{2}  is the smallest positive factor of  k . 
 
The smallest factor of a positive integer is 1. So, we are given that  \frac{k}{2}=1 , which gives  k=2 . Sufficient.

Answer: D

Hatakekakashi · Answer

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

Bunuel · Answer

Writing Mathematical Formulas on the Forum: https://gmatclub.com/forum/rules-for-po ... l#p1096628

KSBGC · Answer

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.

GMATinsight · Answer

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

Mo2men · Answer

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

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Aks111 · Answer

Some questions make you wonder how brilliant the author of question is. This is one those questions, excellently phrased and makes you think about the concepts you learned. Lovely !

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

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