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If 243^x*463^y = n, where x and y are positive integers

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If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 02 Oct 2010, 03:44
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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
[Reveal] Spoiler: OA
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Re: equations [#permalink] New post 02 Oct 2010, 03:56
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If 243^x*463^y =n, where x and y are positive integers, what is the units digit of n?

The units digit of 243^x is the same as the units digit of 3^x and similarly the units digit of 463^y is the same as the units digit of 3^y, so the units digit of 243^x*463^y equals to the units digit of 3^x*3^y=3^{x+y}. So, knowing the value of x+y is sufficient to determine the units digit of n.

(1) x + y = 7. Sufficient. (As cyclicity of units digit of 3 in integer power is 4, units digit of 3^7 would be the same as of units digit of 3^3 which is 7)

(2) x=4. No info about y. Not sufficient.

Answer: A.

Hope it helps.
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Re: equations [#permalink] New post 03 Oct 2010, 08:50
Yup!! A it is....equation can be treated like 3^x*3^y hence (x+y)'s value can provide us the last digit...
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Re: If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 10 Sep 2013, 23:57
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Re: If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 03 Mar 2014, 04:18
I have a doubt. Cyclicity of unit digit of 3 is 4. Hence we know that every fourth power of 3 (3^4, 3^8, 3^12) will have the same unit digit, 1. Hence when option B says x = 4, knowing that x and y are positive integers, we know that xy will be a multiple of 4. Unit digit of 3^4k is always 1 isn't it? Shouldn't this be sufficient information?

Shouldn't the answer be D?
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Re: If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 03 Mar 2014, 04:21
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siriusblack1106 wrote:
I have a doubt. Cyclicity of unit digit of 3 is 4. Hence we know that every fourth power of 3 (3^4, 3^8, 3^12) will have the same unit digit, 1. Hence when option B says x = 4, knowing that x and y are positive integers, we know that xy will be a multiple of 4. Unit digit of 3^4k is always 1 isn't it? Shouldn't this be sufficient information?

Shouldn't the answer be D?


I think you are missing that 3^x*3^y=3^{x+y}, so the exponent is x+y not xy.

Does this make sense?
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Re: If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 03 Mar 2014, 04:26
Yes! Can't believe I just made that mistake. Such mistakes are gonna cost me. :/
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Re: If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 03 Mar 2014, 04:28
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siriusblack1106 wrote:
Yes! Can't believe I just made that mistake. Such mistakes are gonna cost me. :/


Yes, careless errors are the #1 cause of score drops on the GMAT! They cause you to miss easier questions, hurting your score a lot more than not know how to solve the harder ones. So, be more careful, before you submit your answer, double-check that it’s the answer to the proper question.
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Re: If 243^x*463^y = n, where x and y are positive integers [#permalink] New post 18 May 2014, 08:53
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243 = 3^5

463 ends with a 3. So we have to know how many times we will multiply 3's at the end of each numbers.

1) 7 times - SUF
2) we dont know Y - INSUF

Choose (a)
Re: If 243^x*463^y = n, where x and y are positive integers   [#permalink] 18 May 2014, 08:53
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