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

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If 243^x*463^y = n, where x and y are positive integers, wha [#permalink]

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29 Mar 2008, 21:11
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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

Last edited by Bunuel on 12 Jul 2013, 01:45, edited 2 times in total.
Edited the question and added the OA
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 21:17
[Edited]

The question was entered as (243)x(463)y initially. Please ignore this post.

Last edited by purefocus428 on 17 Apr 2008, 18:51, edited 1 time in total.
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 21:26
suntaurian wrote:
Came across this interesting question. Thought I will share with you guys....

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

Edited the question to properly indicate that its 243^x and 463^y.. Sorry about that...
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 21:34
purefocus428 wrote:
(243)x(463)y has the same units digit as 3x3y or 9xy.

(1) x + y = 7
x and y could be (0,7) or (2,5) which would give different answers
INSUFF

(2) x = 4
No way of knowing what y is,
INSUFF

(1 and 2) Since x+y = 7, the fact that x = 4 means that y is 3.
9(4)(3) gives a units digit of 8

(C)

Keep trying...Will post the OA after few others have tried as well...
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 22:47
suntaurian wrote:
Came across this interesting question. Thought I will share with you guys....

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

looking at unit digit
3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3
3^6 = 9

1) sufficient - any combinations of x and y will result in unit digit of 7
i.e. x=1 y=6; unit digit = 3*9=7
x=2, y=5; unit digit = 9*3=7
x=3, y=4; unit digit = 7*1=7
also vice versa

2) not sufficient, we need to know y in this case

I'd go with A
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 23:11
suntaurian wrote:
suntaurian wrote:
Came across this interesting question. Thought I will share with you guys....

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

Edited the question to properly indicate that its 243^x and 463^y.. Sorry about that...

A is suff since the last digit of either of the number is 3.
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 23:32
Ah, well that changes the question now that I know they are exponents

I would still do same approach where I believe that only the units digits make a difference.

(243)^x(463)^y has the same units digit as (3^x)(3^y) or 3^(x+y)

Since Statement 1 gives the value of x+y as seven, the answer is (A) since statement 2 doesn't help by itself.
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Re: PS: what is the units digit of n ? [#permalink]

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29 Mar 2008, 23:33
suntaurian wrote:
purefocus428 wrote:
(243)x(463)y has the same units digit as 3x3y or 9xy.

(1) x + y = 7
x and y could be (0,7) or (2,5) which would give different answers
INSUFF

(2) x = 4
No way of knowing what y is,
INSUFF

(1 and 2) Since x+y = 7, the fact that x = 4 means that y is 3.
9(4)(3) gives a units digit of 8

(C)

Keep trying...Will post the OA after few others have tried as well...

Please ignore this post. Looks like I answered it at the same time the post was being corrected.
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Re: PS: what is the units digit of n ? [#permalink]

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17 Apr 2008, 18:22
short way to do this is to realize the unit digit of each number is 3..

therefore the unit digit of N= 3^(x+y)=3^7=7

A it is..
Re: PS: what is the units digit of n ?   [#permalink] 17 Apr 2008, 18:22
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