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If (243)^x(463)^y = n, where x and y are positive integers, [#permalink]
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07 Apr 2010, 23:37
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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: if243x463ynwherexandyarepositiveintegers102054.html
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Re: Units digit [#permalink]
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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).



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Re: Units digit [#permalink]
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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??
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Re: Units digit [#permalink]
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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.



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Re: Units digit [#permalink]
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08 Apr 2010, 02:02
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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.
Hence correct answer is (A).



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Re: Units digit [#permalink]
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08 Apr 2010, 02:52



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Re: Units digit [#permalink]
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08 Apr 2010, 02:54
Bunuel can you please take a look at probabilityquestion84062.html



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Re: Units digit [#permalink]
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08 Apr 2010, 03:57
Thanks Bunuel for providing more info on this one. Kudos



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Re: Units digit [#permalink]
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09 Apr 2010, 23:22
great question .... I made the mistake of choosing C.












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