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What is the units digit of the solution to 177^28 - 133^23?
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02 Jul 2022, 07:07
02 Jul 2022, 07:07
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Question Stats:
90% (01:49) correct
9% (00:44) wrong based on 11 sessions
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What is the units digit of the solution to \(177^{28} - 133^{23}\)?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
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Re: What is the units digit of the solution to 177^28 - 133^23?
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02 Jul 2022, 07:27
02 Jul 2022, 07:27
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Carcass wrote:
What is the units digit of the solution to \(177^{28} - 133^{23}\)?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
These questions can be time-consuming. If you're pressed for time, you can use the following approach to reduce the answer choices to just 2 options in about 5 seconds.
177^(28) - 133^(23) = (odd number)^(some positive integer) - (odd number)^(some positive integer)
= odd - odd
= EVEN
So, the units digit must be EVEN.
Guess C or D and move on.
Cheers,
Brent
What is the units digit of the solution to 177^28 - 133^23?
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01 Aug 2022, 02:31
01 Aug 2022, 02:31
1
It really goes about the cyclic structure of 7^n and 3^n.
You see,
7^1 ends with 7
7^2 ends with 9
7^3 ends with 3
7^4 ends with 1
7^5 ends with 7 again ( which points to the beginning of the cycle and it goes on and on)
.
.
.
So we can infer that 7^28 ends with 1 (because 28 is a multiple of 4)
Similarly,
3^1 ends with 3
3^2 ends with 9
3^3 ends with 7
3^4 ends with 1
3^5 ends with 3 ( which points to the beginning of the cycle)
.
.
.
So we can infer than 3^25 will end with 3 => 3^23 ends with 7
Since, 177^28 is obviously bigger, the difference will be 11 - 7 = 4 ( The 1 being obviously borrowed from the ten's digit place )
Good question
You see,
7^1 ends with 7
7^2 ends with 9
7^3 ends with 3
7^4 ends with 1
7^5 ends with 7 again ( which points to the beginning of the cycle and it goes on and on)
.
.
.
So we can infer that 7^28 ends with 1 (because 28 is a multiple of 4)
Similarly,
3^1 ends with 3
3^2 ends with 9
3^3 ends with 7
3^4 ends with 1
3^5 ends with 3 ( which points to the beginning of the cycle)
.
.
.
So we can infer than 3^25 will end with 3 => 3^23 ends with 7
Since, 177^28 is obviously bigger, the difference will be 11 - 7 = 4 ( The 1 being obviously borrowed from the ten's digit place )
Good question
