It is currently 20 Nov 2017, 23:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 07 Nov 2009
Posts: 303

Kudos [?]: 697 [0], given: 20

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

### Show Tags

07 Apr 2010, 23:37
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

51% (00:59) correct 49% (01:37) wrong based on 36 sessions

### HideShow timer Statistics

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

Kudos [?]: 697 [0], given: 20

Manager
Joined: 10 Aug 2009
Posts: 122

Kudos [?]: 17 [0], given: 13

### Show Tags

07 Apr 2010, 23:43
I'd go with A

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Thus if we know what both x and y are, we can solve it (statement 1).

Kudos [?]: 17 [0], given: 13

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1285

Kudos [?]: 1239 [0], given: 157

Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34

### Show Tags

08 Apr 2010, 00:23
nickk wrote:
I'd go with A

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Thus if we know what both x and y are, we can solve it (statement 1).

So how did you find the values of x & y from Stmt 1??
_________________

Kudos [?]: 1239 [0], given: 157

Manager
Joined: 10 Aug 2009
Posts: 122

Kudos [?]: 17 [0], given: 13

### Show Tags

08 Apr 2010, 00:59
Hussain15 wrote:
nickk wrote:
I'd go with A

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Thus if we know what both x and y are, we can solve it (statement 1).

So how did you find the values of x & y from Stmt 1??

Well we don't know the values of X and Y individually, but all we need to know is how many times a number with 3 in the units digit is multiplied by itself. Since X and Y are both exponents of such numbers, knowing x+y is sufficient.

Of course I might be wrong so the OA would be appreciated.

Kudos [?]: 17 [0], given: 13

Intern
Joined: 04 Apr 2010
Posts: 9

Kudos [?]: 3 [1], given: 0

### Show Tags

08 Apr 2010, 02:02
1
KUDOS
In this case, since the base number is different i.e 243 & 463, it makes sense to use the various combinations of x & y:
1. 1&6 or 6&1
2. 2&5 or 5&2
3. 3&4 or 4&3

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Substituting n in the above combinations and multiplying the ending unit digits of each of these numbers, we get the same unit digit i.e., 7.

Choice (B), keeps the n open for y, so the unit digit of the resultant number may vary.

Kudos [?]: 3 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42275

Kudos [?]: 132869 [3], given: 12389

### Show Tags

08 Apr 2010, 02:52
3
KUDOS
Expert's post
rohitgoel15 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

Units digit of $$243^x$$ equals to units digit of $$3^x$$ and units digit of $$463^y$$ equals to units digit of $$3^y$$ (general rule). Hence units digit of $$243^x*463^y$$ equals to units digit of $$3^x*3^y=3^{x+y}$$. So knowing the value of $$x+y$$ is sufficient to determine units digit of $$n$$.

(1) $$x+y=7$$. Sufficient. (As cyclicity of $$3$$ 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.

_________________

Kudos [?]: 132869 [3], given: 12389

Manager
Joined: 10 Aug 2009
Posts: 122

Kudos [?]: 17 [0], given: 13

### Show Tags

08 Apr 2010, 02:54
Bunuel can you please take a look at probability-question-84062.html

Kudos [?]: 17 [0], given: 13

Intern
Joined: 04 Apr 2010
Posts: 9

Kudos [?]: 3 [0], given: 0

### Show Tags

08 Apr 2010, 03:57
Kudos

Kudos [?]: 3 [0], given: 0

Manager
Joined: 07 Jan 2010
Posts: 236

Kudos [?]: 9 [0], given: 16

### Show Tags

09 Apr 2010, 23:22
great question ....
I made the mistake of choosing C.

Kudos [?]: 9 [0], given: 16

Re: Units digit   [#permalink] 09 Apr 2010, 23:22
Display posts from previous: Sort by