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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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Intern
Joined: 16 Mar 2017
Posts: 13
If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by [#permalink]

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19 Sep 2017, 07:23
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Difficulty:

15% (low)

Question Stats:

67% (00:57) correct 33% (00:53) wrong based on 86 sessions

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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
SC Moderator
Joined: 22 May 2016
Posts: 1759
If k and m are integers and k = m*(m+4)*(m+5), k must be divisible by [#permalink]

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19 Sep 2017, 08:47
2
1
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

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Joined: 25 Feb 2013
Posts: 1142
Location: India
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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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19 Sep 2017, 09:34
2
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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