EgmatQuantExpert wrote:
Question:
If \(a\) is the units digit of \(7^{47}\) and b is the rightmost nonzero digit in \((125^{10}× 28^{15})\). What is the value of \(a+b\)?
A) 1
B) 2
C) 5
D) 6
F) 8
The cyclicity of number 2 and 7 will be needed to solve the question
-n--------1---2---3---4
-2--------2---4---8---6
-7--------7---9---3---1Since a is the units digit of \(7^{47}\), it will be the units digit of \(7^{4*11 + 3}\) or \(7^3\), which is 3.
Similarly, b is the units digit of \((125^{10}× 28^{15})\)
\((125^{10} * 28^{15})\) = \((5^3)^{10} * (2^2 * 7)^{15}\) = \(5^{30}*2^{30}*7^{4*3 + 3}\) = \(10^{30} * 7^{4*3 + 3}\) as \(a^m * b^ m = (ab)^m\)
This will translate to the units digit of \(7^3\) which is 3.
Therefore, the value of a+b is
6(Option D)
_________________
You've got what it takes, but it will take everything you've got