If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?
(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.
The answer is A, assuming that all multiples of 3 are there in the set but actually its nowhere mentioned in the question as to what exactly are the contents of the set!
Not clear on whts being asked
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 429
- Joined: Wed Sep 19, 2012 11:38 pm
- Thanked: 6 times
- Followed by:4 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Statement 1: For any integer in P, the sum of 3 and that integer is also in P.If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?
1) For any integer in P, the sum of 3 and that integer is also in P.
2) For any integer in P, that integer minus 3 is also in P.
In other words, if we ADD 3 to any integer in P, we get ANOTHER INTEGER in P.
Since 3 is in P, 3+3=6 also is in P.
Since 6 is in P, 6+3=9 also is in P.
Since 9 is in P, 9+3=12 also is in P.
And so on.
Thus, every positive multiple of 3 -- {3, 6, 9, 12...} -- is in P.
SUFFICIENT.
Statement 2: For any integer in P, that integer minus 3 is also in P.
In other words, if we SUBTRACT 3 from any integer in P, we get ANOTHER INTEGER in P.
Since 3 is in P, 3-3=0 also is in P.
Since 0 is in P, 0-3=-3 also is in P.
Since -3 is in P, -3-3=-6 also is in P.
And so on.
Thus:
Every multiple of 3 LESS THAN OR EQUAL TO 3 -- {3, 0, -3, -6...} -- is in P.
No way to determine whether any multiples of 3 GREATER THAN 3 are in P.
INSUFFICIENT.
The correct answer is A.
For a similar problem, check here:
https://www.beatthegmat.com/ds-q-70-p-15 ... 48-15.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3