If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?
I.3 II.4 III.6
I.3 II.4 III.6
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Divide evenly problem
Source: Beat The GMAT — Problem Solving |
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thephoenix
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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
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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
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.
.
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.
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thephoenix
- Legendary Member
- Posts: 1560
- Thanked: 137 times
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
