Divide evenly problem
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
thephoenix
- Legendary Member
- Posts: 1560
- Joined: Tue Nov 17, 2009 2:38 am
- Thanked: 137 times
- Followed by:5 members
For any positive integer m, k contains a multiple that is divisible by 6, and since 3 is a factor of 6, it can also evenly divide into any value of k.
m = 1, then k = 1 * (1 + 4) * (1 + 5) = 1 * 5 * 6 --> clearly, you can see that both 3 and 6 can be divided into this.
m =2, then k = 2 * 6 * 7, again you have a factor 6 in there, so you could divide both 3 and 6
.
.
.
say m = 7, then k = 7 * 11 * 12 --> 12 is a multiple of both 6 and 3.
As you can see, for any value of m, there exists a multiple in k that is divisible by 3 or 6.
m = 1, then k = 1 * (1 + 4) * (1 + 5) = 1 * 5 * 6 --> clearly, you can see that both 3 and 6 can be divided into this.
m =2, then k = 2 * 6 * 7, again you have a factor 6 in there, so you could divide both 3 and 6
.
.
.
say m = 7, then k = 7 * 11 * 12 --> 12 is a multiple of both 6 and 3.
As you can see, for any value of m, there exists a multiple in k that is divisible by 3 or 6.
-
adamsmith2009
- Senior | Next Rank: 100 Posts
- Posts: 36
- Joined: Fri Mar 27, 2009 6:53 pm
-
thephoenix
- Legendary Member
- Posts: 1560
- Joined: Tue Nov 17, 2009 2:38 am
- Thanked: 137 times
- Followed by:5 members
i just substitute m with 1,2,3,4,5,6,7....and check for divisbilty with 3,4,6 and concluded that 3,6 is true for all casesRoadtoIVY wrote:Could you please explain? How did you get this?
but 4 is not
