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If an integer n is to be chosen at random from the integers

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If an integer n is to be chosen at random from the integers [#permalink] New post 05 Aug 2006, 07:06
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If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.1/4
B.3/8
C.1/2
D.5/8
E.3/4
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Re: integer [#permalink] New post 05 Aug 2006, 08:58
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ong wrote:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.1/4
B.3/8
C.1/2
D.5/8
E.3/4


Total = 96

n(n+1)(n+2) => consecutive integer.. thus mutiples of 6

if n = even.. then n+2 is even.. =>n(n+1)(n+2) = multiples of 8
the number of even integers in given interval = 96/2 = 48
if n+1 = multiples of 8 also satisfy the condition.
the number of multiples of 8 in given interval = 96/8 = 12

Thus, (48+12)/96 = 5/8

D it is.

Just add 2 more cents..
If u not sure why even consecutive intergers are multiples of 8..
An even integer = 2m
n*(n+2) = 2m(2m+2) = 4m(m+1) : either m or m+1 is even. Thus, always multiples of 8.
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Last edited by freetheking on 05 Aug 2006, 09:25, edited 6 times in total.
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Re: integer [#permalink] New post 05 Aug 2006, 11:33
freetheking wrote:
ong wrote:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.1/4
B.3/8
C.1/2
D.5/8
E.3/4


Total = 96

n(n+1)(n+2) => consecutive integer.. thus mutiples of 6

if n = even.. then n+2 is even.. =>n(n+1)(n+2) = multiples of 8
the number of even integers in given interval = 96/2 = 48
if n+1 = multiples of 8 also satisfy the condition.
the number of multiples of 8 in given interval = 96/8 = 12

Thus, (48+12)/96 = 5/8

D it is.

Just add 2 more cents..
If u not sure why even consecutive intergers are multiples of 8..
An even integer = 2m
n*(n+2) = 2m(2m+2) = 4m(m+1) : either m or m+1 is even. Thus, always multiples of 8.


Your approach is good But
Aren't you double counting multiples of 6 that are also multiples of 8 Such as (24,48,96) ?


Heman
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 [#permalink] New post 05 Aug 2006, 11:36
I didn't count multiples of 6... just counted multiples of 8.

if n = even.. then n+2 is even.. =>n(n+1)(n+2) = multiples of 8
the number of even integers in given interval = 96/2 = 48

if n+1 = multiples of 8 also satisfy the condition.
the number of multiples of 8 in given interval = 96/8 = 12
_________________

The only thing that matters is what you believe.

Manager
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Posts: 101
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Re: integer [#permalink] New post 05 Aug 2006, 19:25
freetheking wrote:
ong wrote:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.1/4
B.3/8
C.1/2
D.5/8
E.3/4


Total = 96

n(n+1)(n+2) => consecutive integer.. thus mutiples of 6

if n = even.. then n+2 is even.. =>n(n+1)(n+2) = multiples of 8
the number of even integers in given interval = 96/2 = 48
if n+1 = multiples of 8 also satisfy the condition.
the number of multiples of 8 in given interval = 96/8 = 12

Thus, (48+12)/96 = 5/8

D it is.

Just add 2 more cents..
If u not sure why even consecutive intergers are multiples of 8..
An even integer = 2m
n*(n+2) = 2m(2m+2) = 4m(m+1) : either m or m+1 is even. Thus, always multiples of 8.

OA is D
excellent explanation
Re: integer   [#permalink] 05 Aug 2006, 19:25
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