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Updated on: 30 Jun 2024, 07:51
Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:57.
Last edited by Bunuel on 30 Jun 2024, 07:51, edited 3 times in total.
Last edited by Bunuel on 30 Jun 2024, 07:51, edited 3 times in total.
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Difficulty:
5%
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Question Stats:
83% (01:14) correct
17%
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wrong
based on 1145
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What is the remainder when |\(5^{13} -6^{14}\)| is divided by 10, where the symbol | | represents the modulus function.
A) 0
B) 1
C) 2
D) 3
E) 4
A) 0
B) 1
C) 2
D) 3
E) 4
27 Feb 2018, 10:48
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EgmatQuantExpert
When a number is divided by 10, then the unit's digit of the number will be the remainder.
\(|5^{13}-6^{14}|=|6^{14}-5^{13}|\)
Now we know that \(5\) raised to any power will have unit's digit of \(5\) and \(6\) raised to any power will have unit's digit \(6\). so \(5^{13}\) will have unit's digit \(5\)
Similarly \(6^{14}\) will have unit's digit \(6\)
so unit's digit of \(|6^{14}-5^{13}|=|6-5|=1\)
Hence the remainder will be \(1\)
Option B
27 Feb 2018, 23:30
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Solution:
We are given an expression and asked to find out the remainder when the expression is divided by \(10\).
- • Per our conceptual knowledge, if a number is divided by \(10\), the remainder is equal to the units digit of the number itself.
- \(5^{13}\)
- o \(5\) has a cyclicity of \(1\)
o So, the units digit in \(5^{13} = 5\) - \(6^{14}\)
- o \(6\) has a cyclicity of \(1\)
o So, the units digit in \(6^{14} = 6\)
Thus, this question is asking us to find the units of the expression.
Now, let us find the units digit of both the numbers.
This means:
• \(|5^{13} – 6^{14}|\) =\(|5 – 6|\) units digit = \(|-1|\)units digit = \(1\)
• Thus, the units digit of \(|5^{13} - 6^{14}| = 1\)
