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Comment on Units Digit of Large Powers
Is this mathematically proven
Yes, I believe that someone
Yes, I believe that someone has proven the concepts/rules described in this video (and in the follow-up video https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1035)
All of this would fall under the heading of modular arithmetic (see https://en.wikipedia.org/wiki/Modular_arithmetic), which examines divisibility and remainders.
Notice that asking for the units digit of some value is the same as asking for the remainder when that value is divided by 10.
For example, when we divide 4257 by 10, the remainder is 7, and when we divide 173 by 10, the remainder is 3
https://gre.myprepclub.com/forum
286 has a cycle of 1, so the unit digit is going to be 6
52^12 has a cycle of 5 i.e the 52^10 = - 2 and 52^12 = -8
6-8 = -2
what is wrong here
52^12 has a cycle of 4 (not 5
52^12 has a cycle of 4 (not 5)
Let's check:
52^1 = 52
52^2 = --4
52^3 = --8
52^4 = --6
52^5 = --2
52^6 = --4
52^7 = --8
52^8 = --6
...etc
Cheers,
Brent
I have a quick question at
When raising integers to any
When raising integers to any power, there are only three possible cycles:
Cycle of 1: This occurs when the units digit is 0, 1, 5 or 6
Cycle of 2: This occurs when the units digit is 4 or 9
Cycle of 4: This occurs when the units digit is 2, 3, 7 or 8
To better understand why 53 has a cycle of 4, let's examine some powers of 53.
53^1 = 53
53^2 = 2809
53^3 = ----7
53^4 = ----1
53^5 = ----3
53^6 = ----9
53^7 = ----7
53^8 = ----1
53^9 = ----3
Etc.
We can see that the pattern is: 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1
Does that help?
Cheers,
Brent
Hi Brent,
in https://gre.myprepclub.com/forum/units-digit-of-n-in-comparison-of-2769.html
In your explination : 52^(12)= means 2^(12)...2^(4*3) will have same Cyclicity as 2^4 hence 6..
here I didnt get how are you calculating 52^12 as 2^12 ..
Could you please explain me in an eloborate way.
Thank You
Question link: https:/
Question link: https://gre.myprepclub.com/forum/units-digit-of-n-in-comparison-of-2769....
ASIDE: I didn't provide any solutions to this question.
Since we are interested in only the UNITS digit, we can ignore the other digits.
Consider these examples:
12¹ = 12 (units digit 2) and 2¹ = 2 (units digit 2)
12² = 144 (units digit 4) and 2² = 4 (units digit 4)
12³ = 1,728 (units digit 8) and 2³ = 8 (units digit 8)
12⁴ = 20,736 (units digit 6) and 2⁴ = 16 (units digit 6)
12⁵ = 248,832 (units digit 2) and 2⁵ = 32 (units digit 2)
etc
The same applies to any other powers.
For example, 97² has units digit 9, and 7² has units digit 9
73⁴ has units digit 1, and 3⁴ has units digit 1
Does that help?
Cheers,
Brent
Hey Brent how can Quainty A
https://gre.myprepclub.com/forum/qotd-7-n-824-x-where-x-is-a-positive-integer-2656.html
Like it asked for number of possible values which is 2 as the cycle but can u tell me how can the question stem be phrased that makes the answer D like 4 or 6 vs quantity B 4
Question link: https://gre
Question link: https://gre.myprepclub.com/forum/qotd-7-n-824-x-where-x-is-a-positive-in...
One way to reword the question so that the answer is D is to make Quantity A "The units digit of N," in which case Quantity A can be 4 or 6.
When Quantity A is 4, the two quantities are equal.
When Quantity A is 6, Quantity A is greater.
Answer: D
The first practice question
Here: https://gre.myprepclub.com/forum/which-of-the-following-could-be-the-units-digit-98-x-5817.html
... is kind of a confusing mess.
There was a typo in the original question.
You answered that original question.
That is, you answered the original
(with typo) question:
What is the units digit of 98^x?
That number, corrected, is actually composed of "stacked" exponents:
What is the units digit of
9^(8)^x
The corrected typo makes a huge difference in the answer, I think.
I think the correct answer is 1 (only, of all 10 possibilities).
8^(anything) = even
9^even = units digit 1
I cannot see the "official" answer [not logged in], but if you look at the last five posts on the thread, the mod posts two contradictory answers.
Your answer for the original question is C, E, G, I
I think that the currently correct answer is B) 1
Am I missing something?
Or is 1 now the correct answer?
You're absolutely right. If
You're absolutely right. If the power is 9^8^x, then the units digit is always 1. (not why the question was changed, but the OA is still given as C, E, G, I (which is now incorrect)