If k is a positive integer, is k a prime number?
(1) No integers between 2 and k√k, inclusive divides k evenly.
(2) No integers between 2 and k/2 inclusive divides k evenly, and k is greater than 5.
OA: D
If k is a positive integer
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 366
- Joined: Fri Jun 05, 2015 3:35 am
- Thanked: 3 times
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Bumping for experts reviewNandishSS wrote:If k is a positive integer, is k a prime number?
(1) No integers between 2 and k√k, inclusive divides k evenly.
(2) No integers between 2 and k/2 inclusive divides k evenly, and k is greater than 5.
OA: D
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
We are given that k is a positive integer and need to determine whether k is prime. Recall the following:NandishSS wrote:If k is a positive integer, is k a prime number?
(1) No integers between 2 and k√k, inclusive divides k evenly.
(2) No integers between 2 and k/2 inclusive divides k evenly, and k is greater than 5.
If no integers between 2 and √k, inclusive, divide k evenly, then k is a prime.
For example, 17 is a prime since none of the integers 2, 3, and 4 (notice that √17 ≈ 4.1) divide 17 evenly.
Statement One Alone:
No integers between 2 and k√k, inclusive divides k evenly.
Since no integers between 2 and k√k, inclusive divide k evenly, it must be true that no integers between 2 and √k (notice that √k < k√k), inclusive, divide k evenly. So k must be a prime. Statement one alone is sufficient.
Statement Two Alone:
No integers between 2 and k/2 inclusive divides k evenly, and k is greater than 5.
Since no integers between 2 and k/2, inclusive, divide k evenly, it must be true that no integers between 2 and √k (notice that √k < k/2 when k > 5), inclusive, divide k evenly. So k must be a prime. Statement two alone is also sufficient.
Answer: D
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews