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Re: Units Digit of n in comparison of 0 [#permalink]
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yasir9909 wrote:
\(286^1^0-52^1^2=n\)

Quantity A
Quantity B
The units digit of n
0



    A : Quantity A is greater
    B : Quantity B is greater
    C : Both quantities are equal
    D : Answer Cannot be determined


Units digit have a Cyclicity which can be found for any number..
If you have an integer, only the units digit of any power to that number is dependent only on the units digit of the base...
For example.. 23678^9 ..the units digit will depend on units digit of base 23678.

All number will surely repeat unit digits after every fourth, although few don't change at all and few have Cyclicity after two..
(1) Same units digit always..
1...1^2=1^3=1^4=1..
5....\(5^1=5....5^2=25....5^3=125\), thus 5 every time
6.....\(6^1=6...6^2=36.....6^3=216\), thus 6 every time
0....0 every time..

(2) Cyclicity after two..
4...\(4^1=4...4^2=16...4^3=64\), thus 4,6,4,6..
9....\(9^1=9....9^2=81....9^3=729\), thus 9,1,9,1..

(3) Cyclicity after 4..
2.....2,4,8,6,2,4..
3....3,9,7,1,3,9...
7....7,9,3,1,7,9...
8.....8,4,2,6,8,4,2...


Here we have \(286^1^0-52^1^2=n\)
286 means 6 and 6 will have 6 as units digit always..
52^(12)= means 2^(12)...2^(4*3) will have same Cyclicity as 2^4 hence 6..

So units digit of n will be 6-6=0..
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Re: Units Digit of n in comparison of 0 [#permalink]
something wrong in question. one need to edit - 0 extent is incorrect
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Re: Units Digit of n in comparison of 0 [#permalink]
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Fix this question please
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Re: Units Digit of n in comparison of 0 [#permalink]
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HappyMathtutor wrote:
Fix this question please



I hope it is better
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Re: Units Digit of n in comparison of 0 [#permalink]
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Re: Units Digit of n in comparison of 0 [#permalink]
yasir9909 wrote:
\(286^{10}-52^{12}=n\)

Quantity A
Quantity B
The units digit of n
0



    A : Quantity A is greater
    B : Quantity B is greater
    C : Both quantities are equal
    D : Answer Cannot be determined


----------CONCEPT--------------------
2power1, 2power5, 2power9, 2power13 all have unit digit as 2
2power2, 2power6, 2power10, 2power14 all have unit digit as 4
2power3, 2power7, 2power11, all have unit digit as 8
2power4, 2power8, 2power12 all have unit digit as 6

Basically each unit digit among (2,4,6,8) in 2power'x' repeats after a power of 4 in their respective series.
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Re: Units Digit of n in comparison of 0 [#permalink]
Hello from the GRE Prep Club BumpBot!

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Re: Units Digit of n in comparison of 0 [#permalink]
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