Author
Message
TAGS:
Senior Manager

Joined: 06 Jul 2006

Posts: 295

Location: SFO Bay Area

Schools: Berkeley Haas

Followers: 2

Kudos [? ]:
31
[0 ] , given: 0

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

Question Stats:

47% (01:37) correct

53% (01:48) 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

Manager

Joined: 27 Mar 2008

Posts: 53

Followers: 1

Kudos [? ]:
6
[0 ] , given: 0

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.

Senior Manager

Joined: 06 Jul 2006

Posts: 295

Location: SFO Bay Area

Schools: Berkeley Haas

Followers: 2

Kudos [? ]:
31
[0 ] , given: 0

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...

Senior Manager

Joined: 06 Jul 2006

Posts: 295

Location: SFO Bay Area

Schools: Berkeley Haas

Followers: 2

Kudos [? ]:
31
[0 ] , given: 0

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...

Manager

Joined: 20 Aug 2007

Posts: 66

Followers: 1

Kudos [? ]:
7
[0 ] , given: 0

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

CEO

Joined: 29 Aug 2007

Posts: 2501

Followers: 53

Kudos [? ]:
506
[0 ] , given: 19

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.

_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html Math: new-to-the-math-forum-please-read-this-first-77764.html Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html GT

Manager

Joined: 27 Mar 2008

Posts: 53

Followers: 1

Kudos [? ]:
6
[0 ] , given: 0

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.

Manager

Joined: 27 Mar 2008

Posts: 53

Followers: 1

Kudos [? ]:
6
[0 ] , given: 0

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.

Current Student

Joined: 28 Dec 2004

Posts: 3404

Location: New York City

Schools: Wharton'11 HBS'12

Followers: 13

Kudos [? ]:
159
[0 ] , given: 2

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

Similar topics
Author
Replies
Last post
Similar Topics:

2
If 243^x*463^y = n, where x and y are positive integers, wha
mattapraveen
4
05 Nov 2010, 03:05

7
If 243^x*463^y = n, where x and y are positive integers
anilnandyala
8
02 Oct 2010, 03:44

4
If (243)^x(463)^y = n, where x and y are positive integers,
rohitgoel15
8
07 Apr 2010, 22:37

If (243)x(463)y = n, where x and y are positive integers,
ldpedroso
11
27 May 2008, 18:45

If (243)^x * (463)^y = n, where x and y are positive
jimjohn
5
30 Oct 2007, 10:54