GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If n is a positive integer, for which of the following would the units
[#permalink]
12 Feb 2021, 06:41
12 Feb 2021, 06:41
Expert Reply
00:00
Question Stats:
40% (01:30) correct
60% (01:44) wrong based on 10 sessions
Hide Show timer Statistics
If \(n\) is a positive integer, for which of the following would the units digit always be equal to the units digit of \(n\)?
A. \(n^5\)
B. \(n^{10}\)
C. \(n^{25}\)
Kudos for the right answer and explanation
A. \(n^5\)
B. \(n^{10}\)
C. \(n^{25}\)
Kudos for the right answer and explanation
Re: If n is a positive integer, for which of the following would the units
[#permalink]
12 Feb 2021, 08:50
12 Feb 2021, 08:50
1
Hi,
This question can be solved using cyclicity. Cyclicity of any number is about the last digit and how they appear in a certain defined manner.
1 has a cyclicity of 1
2 has a cyclicity of 4 i.e. 2, 4, 8, 6 and then the units digit repeats
3 has a cyclicity of 4
4 has a cyclicity of 2 and so on..
Now, inorder to find the answer to the above question wee need the units digit to be same as the units digit of n.
The maximum cyclicity that a number has is of 4 and the minimum being 1
Thus, if I consider 4 as the cyclicity, then the 5th time in multiply the number by itself it would give me the same units digit , similarly for a cyclicity of 2 and 1. And in the same way, when I multiply the number for 25th time it would give me the same units digit.
IMO A & C
Hope this helps!
This question can be solved using cyclicity. Cyclicity of any number is about the last digit and how they appear in a certain defined manner.
1 has a cyclicity of 1
2 has a cyclicity of 4 i.e. 2, 4, 8, 6 and then the units digit repeats
3 has a cyclicity of 4
4 has a cyclicity of 2 and so on..
Now, inorder to find the answer to the above question wee need the units digit to be same as the units digit of n.
The maximum cyclicity that a number has is of 4 and the minimum being 1
Thus, if I consider 4 as the cyclicity, then the 5th time in multiply the number by itself it would give me the same units digit , similarly for a cyclicity of 2 and 1. And in the same way, when I multiply the number for 25th time it would give me the same units digit.
IMO A & C
Hope this helps!
gmatclubot
Re: If n is a positive integer, for which of the following would the units [#permalink]
12 Feb 2021, 08:50
Moderators:
