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30 Nov 2021, 06:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (03:13) correct
38%
(02:48)
wrong
based on 128
sessions
History
Date
Time
Result
Not Attempted Yet
A number m is randomly selected from the set {11,13,15,17,19}, and a number n is randomly selected from {1999,2000,2001,...,2018}. What is the probability that \(m^n\) has a units digit of 1?
(A) \(\frac{1}{5}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{3}{10}\)
(D) \(\frac{7}{20}\)
(E) \(\frac{2}{5}\)
(A) \(\frac{1}{5}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{3}{10}\)
(D) \(\frac{7}{20}\)
(E) \(\frac{2}{5}\)
24 Dec 2021, 02:58
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Bunuel
Generate favorable and unfavorable cases for each value of \(m^n\).
m = 11
11 raised to any value of n will have 1 as unit digit.
Since there are 20 possible values of n,
Favorable case = 20
Unfavorable = 0
m = 13
Cyclicity of 13 is 4.Any number of the form \(13^{4x}\) will have 1 as unit digit.
Favorable case = 5 {2000,2004,2008,2012,2016}
Unfavorable = 15
m = 15
15 raised to anything will have 5 as unit digit
Favorable case = 0
Unfavorable = 20
m = 17
Cyclicity of 17 is 4.Any number of the form \(17^{4x}\) will have 1 as unit digit.
Favorable case = 5 {2000,2004,2008,2012,2016}
Unfavorable = 15
m = 19
Cyclicity of 19 is 2.Any number of the form \(19^{2x}\) will have 1 as unit digit.
Favorable case = 10 {2000,,2002,2004,2006,2008,,2010,2012,2014,2016,2018}
Unfavorable = 10
Required probability = Favorable/(Favorable + Unfavorable)
=40/(40+60)
=40/100
=2/5
General Discussion
21 Apr 2025, 00:32
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