Remainder when 3^(4n+2) is divided by 10

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g_beatthegmat: Master | Next Rank: 500 Posts; Posts: 100; Joined: Fri Jul 27, 2007 12:36 pm; Thanked: 6 times

Remainder when 3^(4n+2) is divided by 10

by g_beatthegmat » Tue Jun 17, 2008 9:43 am

Encountered this question in the GMAT Prep questions. Please have a look at the attached screenshot.

I feel the answer should be (D) and not (A) or (B) because irrespective of the answer choices, the answer is already available from the question itself.

What say?

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Source: Beat The GMAT — Data Sufficiency | Tue Jun 17, 2008 9:43 am

Motherjane: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Sun Jun 15, 2008 10:50 pm; Thanked: 4 times

Re: Remainder when 3^(4n+2) is divided by 10

by Motherjane » Tue Jun 17, 2008 10:02 am

g_beatthegmat wrote:Encountered this question in the GMAT Prep questions. Please have a look at the attached screenshot.

I feel the answer should be (D) and not (A) or (B) because irrespective of the answer choices, the answer is already available from the question itself.

What say?

I thought the answer would be A. The question was to find the distinct value of the remainder. Its only from statement 1 that we know abt the value of n and hence the remainder.

Statement 2 is irrelevant as the equation has nothing to do with 'm'.

Hence (A).

We need some more opinions

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g_beatthegmat: Master | Next Rank: 500 Posts; Posts: 100; Joined: Fri Jul 27, 2007 12:36 pm; Thanked: 6 times

by g_beatthegmat » Tue Jun 17, 2008 10:11 am

Ah, that's what I though too and marked (A) as the answer while appearing for the prep test. But here's the catch -

From the question, we have 3^(4n+2) / 10.

Numerator
3^(4n+2) can also be written as
=>3^(4n) * 3^2
=>3^(4n) * 9
=>(3^4)^n * 9 { (3^4)^n is same as 3^(4n) }
=>81^n * 9

Now we've reached to a point where we're actually not dependent on n because anything to the power of 81 would end with unit's digit of 1. So value of n does not matter.

But when we multiply the number with unit's digit of 1 with 9, we would get unit's digit as 9. And when this number is divided by 10, the remained is always 9.

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atlantic: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Apr 27, 2008 10:31 am; Location: Portugal; Thanked: 7 times

by atlantic » Tue Jun 17, 2008 10:31 am

Hi g_beatthegmat,

In fact from the statement we can determine the remainder. Remind that the powers of three are cyclic. Every four numbers you get always the same units digit number.

In this case, since 'n' is an integer we know that....

n=1 - 3^6
n=2 - 3^10
n=3 - 3^14
.....

The units digit of any of the above powers of three is 9. So my pick would be (F). A new GMAT option for (F) none of the propositions are needed. Lol.

How can B be the correct choice? This one needs an expert. Definitely!

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Motherjane: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Sun Jun 15, 2008 10:50 pm; Thanked: 4 times

Re: Remainder when 3^(4n+2) is divided by 10

by Motherjane » Tue Jun 17, 2008 12:04 pm

g_beatthegmat wrote:Encountered this question in the GMAT Prep questions. Please have a look at the attached screenshot.

I feel the answer should be (D) and not (A) or (B) because irrespective of the answer choices, the answer is already available from the question itself.

What say?

I agree with you. The answer will be (D). Irrespective of the value of n or m, the remainder will always be 9.

So both n & m does not matter. So both statements are individually sufficient as both individually don't matter.

But if the equation was 3^(4n+m), then the answer would have been (B).