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Units Digit of n in comparison of 0
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Updated on: 30 Jan 2019, 04:39
Updated on: 30 Jan 2019, 04:39
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Question Stats:
50% (01:07) correct
49% (01:20) wrong based on 102 sessions
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\(286^{10}-52^{12}=n\)
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
Re: Units Digit of n in comparison of 0
[#permalink]
04 Oct 2016, 09:44
04 Oct 2016, 09:44
3
Units digit questions are all about patterns.As we are asked about units digit so we need to focus only on units digits of the numbers in equation and we need to find out the pattern that repeats after a certain set of numbers.Therefore,we are only concerned with 6 in 286 and the 2 in 52.
So our new equation should be \(6^1^0-2^1^2 = n\) and we should look for patterns.
Now consider 6 for pattern :
\(6^1 = 6\)
\(6^2 = 36\)
\(6^3 = 216\)
\(6^4 = 1296\)
...
...
...
It may be noted that no matter to what power you raise a number with a 6 as its units digit, the units digit will always be 6
Now consider 2 for pattern :
\(2^1 = 2\)
\(2^2 = 4\)
\(2^3 = 8\)
\(2^4 = 16\)
\(2^5 = 32\)
\(2^6 = 64\)
\(2^7 = 128\)
\(2^8 = 512\)
...
...
...
It may be noted that at \(2^5\) the pattern starts over again.So our units digit pattern for 2 is 2,4,8,6
So \(286^1^0-52^1^2 = n\) => \(6^1^0-2^1^2 = n\) => \(6-6 = n\) => \(n = 0\).
=> the units digit of n is 0,therefore answer is C i.e. Quantity A = Quantity B
This question has been taken from tests of Greatest Prep.Here is the link to the website of Greatest Prep : http://www.greatestprep.com
So our new equation should be \(6^1^0-2^1^2 = n\) and we should look for patterns.
Now consider 6 for pattern :
\(6^1 = 6\)
\(6^2 = 36\)
\(6^3 = 216\)
\(6^4 = 1296\)
...
...
...
It may be noted that no matter to what power you raise a number with a 6 as its units digit, the units digit will always be 6
Now consider 2 for pattern :
\(2^1 = 2\)
\(2^2 = 4\)
\(2^3 = 8\)
\(2^4 = 16\)
\(2^5 = 32\)
\(2^6 = 64\)
\(2^7 = 128\)
\(2^8 = 512\)
...
...
...
It may be noted that at \(2^5\) the pattern starts over again.So our units digit pattern for 2 is 2,4,8,6
So \(286^1^0-52^1^2 = n\) => \(6^1^0-2^1^2 = n\) => \(6-6 = n\) => \(n = 0\).
=> the units digit of n is 0,therefore answer is C i.e. Quantity A = Quantity B
This question has been taken from tests of Greatest Prep.Here is the link to the website of Greatest Prep : http://www.greatestprep.com
Re: Units Digit of n in comparison of 0
[#permalink]
31 Dec 2018, 23:34
31 Dec 2018, 23:34
Please correct the question. 2^8 = 256 not 512
