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02 Oct 2010, 04:44
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:35) correct
41%
(01:44)
wrong
based on 1673
sessions
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Not Attempted Yet
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
(1) x + y = 7
(2) x = 4
02 Oct 2010, 04:56
Kudos
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If \(243^x*463^y =n\), where x and y are positive integers, what is the units digit of n?
The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).
(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power 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.
Hope it helps.
The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).
(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power 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.
Hope it helps.
General Discussion
03 Mar 2014, 05:18
Kudos
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I have a doubt. Cyclicity of unit digit of 3 is 4. Hence we know that every fourth power of 3 (3^4, 3^8, 3^12) will have the same unit digit, 1. Hence when option B says x = 4, knowing that x and y are positive integers, we know that xy will be a multiple of 4. Unit digit of 3^4k is always 1 isn't it? Shouldn't this be sufficient information?
Shouldn't the answer be D?
Shouldn't the answer be D?
