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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
The tens digit of 6^17 is
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09 Jul 2021, 08:27
09 Jul 2021, 08:27
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52% (01:41) correct
47% (01:51) wrong based on 17 sessions
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Retired Moderator
Joined: 16 Apr 2020
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Posts: 1546
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The tens digit of 6^17 is
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11 Jul 2021, 03:55
11 Jul 2021, 03:55
2
GeminiHeat wrote:
The tens digit of 6^17 is
A. 1
B. 3
C. 5
D. 7
E. 9
A. 1
B. 3
C. 5
D. 7
E. 9
\(6^2 = 36\)
\(6^3 = 216\)
\(6^4 = 1296\)
\(6^5 = 7776\)
\(6^6 = 56656\)
\(6^7 = 279936\)
We have a pattern of: 3, 1, 9, 7, 5
i.e. the digits would repeat every 5 terms
3 as ten's digit: \(6^2, 6^7, 6^{12}, 6^{17}, ....\)
1 as ten's digit: \(6^3, 6^8, 6^{13}, 6^{18}, ....\)
9 as ten's digit: \(6^4, 6^9, 6^{14}, 6^{19}, ....\)
7 as ten's digit: \(6^5, 6^{10}, 6^{15}, 6^{20}, ....\)
5 as ten's digit: \(6^6, 6^{11}, 6^{16}, 6^{21}, ....\)
Hence, option B
General Discussion
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The tens digit of 6^17 is
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13 Sep 2024, 20:51
13 Sep 2024, 20:51
1
We need to find the tens digit of 6^17
Last Two digits of 6 follow following pattern
=> So, from 6^2 cycle of tens' digit repeats as 3, 1, 9, 7 , 5, 3, 1 9, 7 , 5
=> We have a cycle of 5 from the 2nd term
=> Tens' digit of 6^17 = Now 17 = 1(6^1 not part of cycle) + 15 (cycle of 5*3) + 1 (as cycle starts from 2nd term) = First term of the cycle = 3
So, Answer will be B
Hope it helps!
Link to Theory for Last Two digits of exponents here.
Link to Theory for Units' digit of exponents here.
Last Two digits of 6 follow following pattern
- Last Two Digits of 6^1 = 06
Last Two Digits of 6^2 = 36
Last Two Digits of 6^3 = 36*6 = 16
Last Two Digits of 6^4 = 16*6 = 96
Last Two Digits of 6^5 = 96*6 = 76
Last Two Digits of 6^6 = 76*6 = 56
Last Two Digits of 6^7 = 56*6 = 36 [ same as 6^2 ]
Last Two Digits of 6^8 = 36*6 = 16 [ same as 6^3 ]
=> So, from 6^2 cycle of tens' digit repeats as 3, 1, 9, 7 , 5, 3, 1 9, 7 , 5
=> We have a cycle of 5 from the 2nd term
=> Tens' digit of 6^17 = Now 17 = 1(6^1 not part of cycle) + 15 (cycle of 5*3) + 1 (as cycle starts from 2nd term) = First term of the cycle = 3
So, Answer will be B
Hope it helps!
Link to Theory for Last Two digits of exponents here.
Link to Theory for Units' digit of exponents here.
