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B
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Difficulty:
25%
(medium)
Question Stats:
76% (01:12) correct
24%
(01:48)
wrong
based on 86
sessions
History
Date
Time
Result
Not Attempted Yet
What is the remainder when \(3^{23} - 23\) is divided by 10?
A. 3
B. 4
C. 5
D. 6
E. 8
A. 3
B. 4
C. 5
D. 6
E. 8
12 Nov 2022, 09:58
Kudos
Bookmarks
Asked: What is the remainder when \(3^{23} - 23\) is divided by 10?
The remainder when \(3^{23} - 23\) is divided by 10
= The remainder when \(3^{2*11+1} - 3\) is divided by 10
= The remainder when \(3*9^{11} - 3\) is divided by 10
= The remainder when \(3*(-1)^{11} - 3\) is divided by 10
= The remainder when \(-3 - 3\) is divided by 10
= 10 - 6 = 4
IMO B
The remainder when \(3^{23} - 23\) is divided by 10
= The remainder when \(3^{2*11+1} - 3\) is divided by 10
= The remainder when \(3*9^{11} - 3\) is divided by 10
= The remainder when \(3*(-1)^{11} - 3\) is divided by 10
= The remainder when \(-3 - 3\) is divided by 10
= 10 - 6 = 4
IMO B
rajtare
Joined: 05 Nov 2014
Last visit: 18 Feb 2026
Posts: 183
Given Kudos: 12
Location: India
Concentration: Operations, Leadership
Schools: Sloan '26 Columbia CBS'26 Goizueta '26 Kellogg '26
GPA: 3.99
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12 Nov 2022, 12:40
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Afroditee
This question is asking us to find the last digit of the number.
Last digit of each power of 3 is given as
3^1 =3
3^2 =9
3^3= 7
3^4 =1
--------
3^5=3
Thus three has a cyclicality of 4. Last digit of 3^23 will be same as last digit of 3^3= 7
thus 3^23 = xxxxx7
now when 23 is subtracted from above number last digit will be 4
xxxxx7-23 = 4
thus remainder will be 4 when divided by 10
hence B
