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21 Aug 2019, 00:48
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:16) correct
30%
(01:21)
wrong
based on 214
sessions
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Date
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If \(x = 103^{103} + 3^{95}\), what is the units digit of x?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
Bunuel
Given: \(x = 103^{103} + 3^{95}\)
Asked: What is the units digit of x?
Unit digit of x
= Unit digit of 103^{103} + 3^{95}[/m]
= Unit digit of \((100+3)^{4*25+3} + 3^{4*23+3}\)
= Unit digit of \((3^3 + 3^3)\) Since \(3^4 = 81\) has unit digit of 1
= Unit digit of 54 = 4
IMO E
21 Aug 2019, 01:05
Kudos
Bookmarks
If x=103^(103) +3^(95)
, what is the units digit of x?
Units digit of 103^(103) = 3^(103)
Now units digits : 3^1 =3, 3^2 =9 , 3^3= 7 ,3^4=1
Now cyclicity of 4 such as 3,9,7,1
103/4 has remainder of 3, so unit digit of 103^(103)= 3^3 =7
95/4 has remainder of 3 ,so unit digit of 3^95 =3^3 =7
Now unit digit of x = 7+7 =14
Answer E
Posted from my mobile device
, what is the units digit of x?
Units digit of 103^(103) = 3^(103)
Now units digits : 3^1 =3, 3^2 =9 , 3^3= 7 ,3^4=1
Now cyclicity of 4 such as 3,9,7,1
103/4 has remainder of 3, so unit digit of 103^(103)= 3^3 =7
95/4 has remainder of 3 ,so unit digit of 3^95 =3^3 =7
Now unit digit of x = 7+7 =14
Answer E
Posted from my mobile device
