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# can anyone explain this clearly ?

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Manager
Joined: 25 Mar 2008
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can anyone explain this clearly ? [#permalink]

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03 Apr 2008, 08:16
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GMAT prep

DS Question:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10.

(1) n = 2
(2) m = 1

pls explain this clearly

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CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4590 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: can anyone explain this clearly ? [#permalink]

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03 Apr 2008, 08:45
1
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Expert's post
Ok.

1. It is obviously that with knowledge of n and m we will have one integer and one reminder. So, C works good. But what about A and B? Maybe GMAT want to trick us with C-Trap?

2. take a look on m. It is definitely clear that at m=2 and m=3 we will have different reminders. So the second condition is necessary.

3. What about the first condition? First of all we have 4*n instead of n and it is a small prompt to dig deeper.

4. What do the reminder mean here? when we divide an integer by 10 we will get a reminder that is equal to the unit digit of the integer. So, the unit digit.....and power......

5. Let write unit digits of some powers of 3:

3^0=1
3^1=3
3^2=9
3^3=7
3^4=1
3^5=3
3^6=9
3^7=7

6. What do we see here? period 4 !!! the unit digit is defined by the reminder of the power divided by 4. Actually reminder of 4n+2 is always 2. So, we have found a trap! the answer is B
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Kudos [?]: 4590 [1], given: 360

Senior Manager
Joined: 20 Dec 2004
Posts: 252

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Re: can anyone explain this clearly ? [#permalink]

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03 Apr 2008, 15:21
Walker,

You really have a lot of patience...hats off to you...

+1 for all your hard work and support to the forum...

Thanks a ton!!!
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Stay Hungry, Stay Foolish

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Re: can anyone explain this clearly ?   [#permalink] 03 Apr 2008, 15:21
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