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D
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Difficulty:
55%
(hard)
Question Stats:
47% (01:09) correct
53%
(01:39)
wrong
based on 209
sessions
History
Date
Time
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If m and n are positive integers. What is the units digit of p^(m*n) ?
(1) The units digit of p^m is 1
(2) The units digit of p^n is 1
Can somebody please explain ?
Thanks
(1) The units digit of p^m is 1
(2) The units digit of p^n is 1
Can somebody please explain ?
Thanks
23 Jul 2013, 15:14
Kudos
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If m and n are positive integers. What is the units digit of p^(m*n) ?
(1) The units digit of p^m is 1 --> \(p^{(m*n)}=(p^m)^n=(...1)^m\) --> the units digit of \((...1)^m\) is 1. Sufficient.
(2) The units digit of p^n is 1 --> \(p^{(m*n)}=(p^n)^m=(...1)^n\) --> the units digit of \((...1)^n\) is 1. Sufficient.
Answer: D.
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3. Thank you.
(1) The units digit of p^m is 1 --> \(p^{(m*n)}=(p^m)^n=(...1)^m\) --> the units digit of \((...1)^m\) is 1. Sufficient.
(2) The units digit of p^n is 1 --> \(p^{(m*n)}=(p^n)^m=(...1)^n\) --> the units digit of \((...1)^n\) is 1. Sufficient.
Answer: D.
Theory on Exponents: math-number-theory-88376.html
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Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html
DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
PS Exponents questions to practice: search.php?search_id=tag&tag_id=60
Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3. Thank you.
23 Jul 2013, 15:20
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Bookmarks
gepetow
hi,
\(p^(m*n)\)= \(p^m^n\) or \(p^n^m\)==> it can be written in both ways...
statement 1: unit digit of\(p^m=1\)
now clearly since p^m==>has unit digit 1 then p^m^n===>will also have unit digit 1
sufficient.
statement 2: The units digit of\(p^n\) is 1
then \(p^n^m\)==>this will have unit digit as one...as both means the same number..as shown above.
sufficient
hence D
please refer to below rules .
Attachments
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