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)
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