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What is the units digit of the solution to
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28 Jan 2021, 03:11
28 Jan 2021, 03:11
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Question Stats:
75% (00:56) correct
25% (02:56) wrong based on 4 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
Kudos for the right answer and explanation
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the units digit of the solution to
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28 Jan 2021, 05:49
28 Jan 2021, 05:49
1
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
Kudos for the right answer and explanation
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
Kudos for the right answer and explanation
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
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01 Feb 2021, 10:23
01 Feb 2021, 10:23
Hi,
We can use cyclicity to solve this question. As 7 has a cyclicity of 4 i.e. 7, 9, 3, &1 and 3 also has a cyclicity of 4 i.e.3, 9, 7 &1
Thus as 28 is divisible by 4 the units digit of 177^28=1 and as 23 is not divisible by 4 we will be left with a remainder of 3. Hence the units digit of 133^23 will be 7. So, 1-7= 6
IMO D
P.s. I do have a detailed post on cyclicity but I am not eligible to add links or attachments.
Hope this helps!!
We can use cyclicity to solve this question. As 7 has a cyclicity of 4 i.e. 7, 9, 3, &1 and 3 also has a cyclicity of 4 i.e.3, 9, 7 &1
Thus as 28 is divisible by 4 the units digit of 177^28=1 and as 23 is not divisible by 4 we will be left with a remainder of 3. Hence the units digit of 133^23 will be 7. So, 1-7= 6
IMO D
P.s. I do have a detailed post on cyclicity but I am not eligible to add links or attachments.
Hope this helps!!
