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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
What is the remainder, after division by 100, of 7^10?
[#permalink]
Updated on: 11 Dec 2022, 14:03
Updated on: 11 Dec 2022, 14:03
1
Expert Reply
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Question Stats:
80% (01:06) correct
20% (02:55) wrong based on 5 sessions
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What is the remainder, after division by 100, of \(7^{10}\)?
(A) 1
(B) 7
(C) 43
(D) 49
(E) 70
(A) 1
(B) 7
(C) 43
(D) 49
(E) 70
Originally posted by GeminiHeat on 10 Dec 2022, 02:11.
Last edited by Carcass on 11 Dec 2022, 14:03, edited 1 time in total.
Last edited by Carcass on 11 Dec 2022, 14:03, edited 1 time in total.
UPDATED
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
What is the remainder, after division by 100, of 7^10?
[#permalink]
12 Dec 2022, 04:34
12 Dec 2022, 04:34
1
Expert Reply
We have such a pattern
7
7*7=49
7*7*7=343
7*7*7*7=...1
7*7*7*7*7=7
So, the last number repeats every 5th time.
10/4 = 2, and the remainder is 2.
we choose 7*7
it means that 7*7*7*7*7*7*7*7*7*7=.......49
We divide by 100, it means .....,49
where 49 is a remainder.
Answer: D
7
7*7=49
7*7*7=343
7*7*7*7=...1
7*7*7*7*7=7
So, the last number repeats every 5th time.
10/4 = 2, and the remainder is 2.
we choose 7*7
it means that 7*7*7*7*7*7*7*7*7*7=.......49
We divide by 100, it means .....,49
where 49 is a remainder.
Answer: D
gmatclubot
What is the remainder, after division by 100, of 7^10? [#permalink]
12 Dec 2022, 04:34
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