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# In the Sequence a1, a2,............a(n),............each

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Director
Joined: 04 Jan 2008
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In the Sequence a1, a2,............a(n),............each  [#permalink]

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20 Jul 2009, 01:09
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In the Sequence a1, a2,............a(n),............each term after the first is 3 greater than the previous term. Is a(100)-1 divisible by 3?

(1)a(99) is indivisible by 3

(2)a1=1

OA....
...........B....OE says..... a99 can be 3n-1 or 3n-2...hence ....INSUFF..i believe its D

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Senior Manager
Joined: 23 Jun 2009
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Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Sequence--Is a(100) -1 divisible by 3?  [#permalink]

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20 Jul 2009, 01:40
B
If all terms are greater than the previous terms by three, it means they all have the same value in (mod 3).
1 insuff. Because we do not know the value of a(99) in (mod 3). It may be 1 or 2. Each choice changes the answer.
2 suff. Since all the terms have same value in (mod 3), a(1)=a(100)=1 in (mod 3). So a(100)-1 is divisible.
Director
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Re: Sequence--Is a(100) -1 divisible by 3?  [#permalink]

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20 Jul 2009, 01:42
maliyeci wrote:
1 insuff. Because we do not know the value of a(99) in (mod 3). It may be 1 or 2. Each choice changes the answer.

got it now
a(99) is 1 or 2

so a(100) becomes 4 or 6

so a(100)-1 becomes 3 or 5

hence INSUFF.
thanks
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Manager
Joined: 07 Apr 2009
Posts: 143
Re: Sequence--Is a(100) -1 divisible by 3?  [#permalink]

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20 Jul 2009, 13:45
Quote:
If all terms are greater than the previous terms by three, it means they all have the same value in (mod 3).

hey can you please throw some light on this statement.
Senior Manager
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Re: Sequence--Is a(100) -1 divisible by 3?  [#permalink]

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21 Jul 2009, 00:03
OK.
a(1)=1, a(2)=4, a(3)=7......a(n)=a(n-1)+3
a(1)=1 in (mod 3)
a(2)=4=1 in mod (3)
a(3)=7=4=1 in mod(3)
For every term you add 3 to previous term. This means in (mod 3) you add a "0" (3 is equal to 0 in mod 3) so every term in this sequence is equal to 1 This is true for other cases (2 and 0)
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Re: Sequence--Is a(100) -1 divisible by 3?  [#permalink]

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21 Jul 2009, 04:54
sure thanks ! i think i got it !

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Re: Sequence--Is a(100) -1 divisible by 3? &nbs [#permalink] 21 Jul 2009, 04:54
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