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If 243^x*463^y = n, where x and y are positive integers, wha [#permalink ]
29 Mar 2008, 20:11

Question Stats:

45% (01:37) correct

55% (01:49) wrong

based on 19 sessions
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
Last edited by

Bunuel on 12 Jul 2013, 00:45, 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 ]
29 Mar 2008, 20:17

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

Last edited by

purefocus428 on 17 Apr 2008, 17:51, edited 1 time in total.

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Re: PS: what is the units digit of n ? [#permalink ]
29 Mar 2008, 20:26

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 ]
29 Mar 2008, 20:34

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 ]
29 Mar 2008, 21:47

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 ]
29 Mar 2008, 22:11

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 ]
29 Mar 2008, 22:32

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 ]
29 Mar 2008, 22:33

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 ]
17 Apr 2008, 17:22

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, 17:22

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