Are there any more practice questions for such type of questions please? Thank you.
Bunuel wrote:
Official Solution:
What is the units digit of \(66^6 - 5^{55}\)?
A. \(0\)
B. \(1\)
C. \(5\)
D. \(6\)
E. \(9\)
A number with the units digit of 6, in any positive integer power, will have 6 as its units digit. So, the units digit of \(66^6\) is 6.
A number with the units digit of 5, in any positive integer power, will have 5 as its units digit. So, the units digit of \(5^{55}\) is 5.
Here, you have to be careful and not assume that the units digit of \(66^6 - 5^{55}\) will be \(6 - 5 = 1\) because you should notice that \(5^{55}\) is MUCH larger number than \(66^6\). Why? \(5^{55}=5^{5*11}=(5^5)^{11}\). Now, \(5^5>66\) and \(11>6\), thus \((5^5)^{11}>66^6\).
Therefore, the units digit of \(66^6 - 5^{55}\) will be \(\{ smaller \ number \ with \ the \ units \ digit \ of \ 6 \} - \{ larger \ number \ with \ the \ units \ digit \ of \ 5\} = 9\). For example, \(16-25=-9\)
Answer: E