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If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by

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If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by [#permalink]

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New post 19 Sep 2017, 07:23
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If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by which of following(s)?

I. 3
II. 6
III. 8

A. I
B. I and II
C. II and III
D. II
E. III
Spoiler: OA
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If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by [#permalink]

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New post 19 Sep 2017, 08:47
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petrified17 wrote:
If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by which of following(s)?

I. 3
II. 6
III. 8

A. I
B. I and II
C. II and III
D. II
E. III

Plug in m = 1, m = 2, m = -7

(1)(5)(6) = 30
divisible by 3 and 6

(2)(6)(7) = 84
divisible by 3 and 6

(-7)(-3)(-2) = -42
divisible by 3 and 6

Answer B
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If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by [#permalink]

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New post 19 Sep 2017, 09:34
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petrified17 wrote:
If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by which of following(s)?

I. 3
II. 6
III. 8

A. I
B. I and II
C. II and III
D. II
E. III


Mathematical approach

\(k=m*(m+4)*(m+5) = (m+3-3)*(m+4)*(m+5)\)

or \(k = (m+3)*(m+4)*(m+5)-3(m+4)*(m+5)\)

Now, \((m+3)\), \((m+4)\) & \((m+5)\) are three consecutive integers, hence MUST be divisible by \(3\) & \(6\)

\(-3(m+4)*(m+5)\), has \(3\) as a factor and \((m+4)\) & \((m+5)\) are consecutive integers, hence either of the two will be a multiple of \(2\). Hence the product MUST be multiple of \(3\) & \(6\)

Therefore \(k\) MUST be divisible by \(3\) & \(6\)

Option B
If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by   [#permalink] 19 Sep 2017, 09:34
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