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If (243)^x(463)^y = n , where x and y are

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If (243)^x(463)^y = n , where x and y are [#permalink]

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If \((243)^x(463)^y = n\), where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-243-x-463-y-n-where-x-and-y-are-positive-integers-102054.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Jul 2013, 00:47, edited 1 time in total.
Edited the question and added the OA
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Re: Digits Manhattan [#permalink]

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New post 08 Oct 2009, 00:29
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sondenso wrote:
If \((243)^x(463)^y = n\), where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4



I added the math formulas to your post :wink:
Just had to hit the M button after highlighting the expression
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Re: Digits Manhattan [#permalink]

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New post 08 Oct 2009, 01:19
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I believe the answer is A.

The units digit of n is equal to the units digit of \(3^x * 3^y = 3^{x+y}\) (If you don't understand why, think about how you multiply two large numbers by hand. The units digit of the product is always the product of the units digit of the numbers being multiplied). So essentially, all we need is x + y.

Statement 1: x + y = 7

Bingo. Sufficient.

Statement 2: x = 4

Doesn't tell us anything about y. Therefore insufficient.
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Re: Digits Manhattan [#permalink]

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New post 08 Oct 2009, 01:54
A it is.
At first i thought it was C. then saw the explanation of AKProdigy87 and understood that it should be A.
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Re: Digits Manhattan [#permalink]

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New post 08 Oct 2009, 07:13
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I agree with A.

If you can't see the simplification you can always work it out by hand.

Write out the series for \(3^x\)

3,9,7,1,3,9,7...

You can quickly see that for every combination of X + Y = 7 it will give the same answer.
If X=1 and Y=6 then you end up with 3 and 9 = 27 (unit digit is 7)
If X=3 and Y=4 then you end up with 7 and 1 = 7 (unit digit is 7)
etc.
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Re: Digits Manhattan [#permalink]

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New post 08 Oct 2009, 19:20
AKProdigy87 wrote:
I believe the answer is A.

The units digit of n is equal to the units digit of \(3^x * 3^y = 3^{x+y}\) (If you don't understand why, think about how you multiply two large numbers by hand. The units digit of the product is always the product of the units digit of the numbers being multiplied). So essentially, all we need is x + y.

Statement 1: x + y = 7

Bingo. Sufficient.

Statement 2: x = 4

Doesn't tell us anything about y. Therefore insufficient.


You are right! Many thanks for all of you (also BB)
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Re: Digits Manhattan [#permalink]

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New post 12 Nov 2009, 10:24
well by looking at the nature of the question even I would have thought it to be A. But one thing I am failing to understand is how are u guys writing 463 as 3 raised to some power of something ? is 463 divisible by 3??

or am i seeing something wrong ?
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Re: Digits Manhattan [#permalink]

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New post 12 Nov 2009, 11:07
mbaquestionmark wrote:
well by looking at the nature of the question even I would have thought it to be A. But one thing I am failing to understand is how are u guys writing 463 as 3 raised to some power of something ? is 463 divisible by 3??

or am i seeing something wrong ?


The only thing to know in this expression is the unit digit of final number, so here "3 raised to some power" is just unit digit of 463 and 243 raised to power X and Y.
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Re: Digits Manhattan [#permalink]

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New post 12 Nov 2009, 18:00
oh yes.. now i get it i guess..

i got confused because smone mentioned the use of http://gmatclub.com/cgi-bin/mimetex.cgi ... E%7Bx+y%7D

thanks..

Shelen wrote:
mbaquestionmark wrote:
well by looking at the nature of the question even I would have thought it to be A. But one thing I am failing to understand is how are u guys writing 463 as 3 raised to some power of something ? is 463 divisible by 3??

or am i seeing something wrong ?


The only thing to know in this expression is the unit digit of final number, so here "3 raised to some power" is just unit digit of 463 and 243 raised to power X and Y.
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Re: Digits Manhattan [#permalink]

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New post 13 Nov 2009, 23:44
it is A. for X+Y = 7, in all combination of x & y the unit digit of n is 7.
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Re: Digits Manhattan [#permalink]

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New post 14 Nov 2009, 03:29
Seeing that the units digits of both 243 and 463 are the same, what the question is really asking is:

What is the units digit of 3^(x+y)?

Therefore the answer is A.
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Re: Digits Manhattan [#permalink]

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New post 05 May 2011, 21:14
using 1,

units digit is 2. Hence A.
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Re: Digits Manhattan [#permalink]

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New post 07 May 2011, 16:31
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1. Sufficient

x+y = 7

units digit = \((3^x)*(3^y)\)

= \((3^(x+y)\)

= 3^7

2. Not sufficient

we dont know anything about y.

Answer is A.
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Re: Digits Manhattan [#permalink]

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New post 15 May 2011, 07:39
Nice question.

The Final answer is 7 and A is sufficient.

A) X+Y = 7 so the last digit 3 is multiplied 7 times leaving the last digit of the final answer as 7.

B) x=4, says nothing about y so insufficient.
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Re: Digits Manhattan [#permalink]

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New post 18 May 2011, 10:32
got it right...
Its A
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Re: Digits Manhattan   [#permalink] 18 May 2011, 10:32
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