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Sequence

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TheRob
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Sequence [#permalink] New post   19 Jun 2009, 07:16
00:00
A
B
C
D
E

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(N/A)

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A certain sequence starts with the number 4. Every sub-sequent term is twice the number 4. Every sub-sequent term is twice the previous one, What is the units digit of the 79 term?

A)8
B)6
C)4
D)2
E)0

I tried to applied the following method

4 firstterm
8 second
16 third
32 fourth
64 fifth
...8 sixth
...6 seventh
...2 eighth
...4 ninth
...8 Tenth

So the Tenth term has a unit digit of 8 I thought that the 80th term would also have a term of 8 so one term less would have 4 the unit-s digit but the answer is D) so what am I doing wrong?



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Re: Sequence [#permalink] New post   19 Jun 2009, 08:06
TheRob wrote:
I tried to applied the following method

4 firstterm
8 second
16 third
32 fourth
64 fifth
...8 sixth
...6 seventh
...2 eighth
...4 ninth
...8 Tenth


I think you are going in the right direction. Last digit of 1st 4 numbers would be 4 (try 4*8*16*32).
Similarly, for product of each subsequent set of 4 numbers, last digit would be 4.

So, this means we have to find last digit of
..4*..4*..4.....(19 times)* ..4 * ..8 *...6

Now, for each 4*4*4, last digit would be 4
This reduces to
..4*..4*..4...(6 times) *4 *..4 * ..8 *...6
=(..4*..4) *..4 *..4 * ..8 *...6
=..4*..4 * ..8 *...6
=..8

So, last digit should be 8, answer A
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Re: Sequence [#permalink] New post   19 Jun 2009, 09:29
It sounds logical however de right answer is D

I will ask the teacher tomorrow and I let you know crapp I almost had the whole homework right
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Re: Sequence [#permalink] New post   21 Jun 2009, 22:11
TheRob wrote:
It sounds logical however de right answer is D

I will ask the teacher tomorrow and I let you know crapp I almost had the whole homework right


Oops, I got it. I read the question incorrectly, and calculated the last digit of the product of the whole series. I'm sure my GMAT score would be reduced due to this habit of mine.

Anyway, the series would be 4, 8, 16, 32, ..4, ..8, ..6, ..2 and so on
That means, the last digit of every 4th term is 2.

The last digit for 79th term would be 6 and 80th term would be 2
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Re: Sequence [#permalink] New post   21 Jun 2009, 22:18
Btw, using my scientific calculator just calculated the value of 79th term of the geometric series, using the formula
nth term = ar^(n-1)

79th term = 1208925819614629174706176
so last digit is 6 only :-D
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Re: Sequence [#permalink] New post   22 Jun 2009, 07:19
I finally found out how to solve this one

Well you can see the pattern

4 first
8 second
16 third
32 fourth

4 fifth

Well you divide 79 / 4

76 / 4 = 19 so in the secuence you will Complete the fourth numbers

and you have a remainder of three so you count

first is 4, second is 8 and the third is 6

this was fun though
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Re: Sequence [#permalink] New post   22 Jun 2009, 16:12
6 is the correct answer.



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Thank you for understanding, and happy exploring!
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Re: Sequence [#permalink]
22 Jun 2009, 16:12
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