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22 Aug 2019, 03:15
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A
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Difficulty:
25%
(medium)
Question Stats:
92% (01:01) correct
8%
(00:06)
wrong
based on 12
sessions
History
Date
Time
Result
Not Attempted Yet
What will be the digit in the unit's place of a single digit which belongs to the set of natural numbers, when this number is raised to the power 5?
a. The number itself
b. Number + 1
c. Number – 1
d. Number / 1
e. None of the above
a. The number itself
b. Number + 1
c. Number – 1
d. Number / 1
e. None of the above
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22 Aug 2019, 06:04
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Simply try 1^5, 2^5, 3^5,...and we can see the pattern that all these results have the same digit in the unit's place like the number itself.
Since we only care about the last digit, we can do it quickly:
1^5=1 => 1
2^5= 32 => 2
3^5 ~ 3^2 *3^2 *3 ~ 9*9*3 ~ 1*3 ~3
4^5 ~ 4^2 * 4^2 * 4 ~ 6*6*4~6*4~4
...
IMO: A
Since we only care about the last digit, we can do it quickly:
1^5=1 => 1
2^5= 32 => 2
3^5 ~ 3^2 *3^2 *3 ~ 9*9*3 ~ 1*3 ~3
4^5 ~ 4^2 * 4^2 * 4 ~ 6*6*4~6*4~4
...
IMO: A
22 Aug 2019, 07:20
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GeorgeKo111
What is the source? Digits are not numbers, so mathematically the question doesn't make sense. I also don't understand the distinction between answer A and answer D; if you divide a number by 1, as we're doing in answer D, you don't change your number, so A and D are the same. Since your units digit never changes if you raise an integer to a 5th power (or 9th, 13th, 17th etc power), both A and D are correct, if I'm understanding the intention behind the problem correctly.
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