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If (243)^x(463)^y = n, where x and y are positive integers, [#permalink]
 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
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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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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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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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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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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. Answer: A.
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Bunuel can you please take a look at probability-question-84062.html
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Thanks Bunuel for providing more info on this one.
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great question ....
I made the mistake of choosing C.
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