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pradeepkaushal9518
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We want the units digit of : (6^15 - 7^4 - 9^3)pradeepkaushal9518 wrote:What is the units digit of 6to power15 - 7to power4 - 9 to power3?
A) 8
B) 7
C) 6
D) 5
E) 4
answer is C but dont know how anyone can explain
The first thing we should note is that there's no way we're expected to actually calculate this giant mess of a number. So, there must be a shortcut.
We think: I only care about the last digit of the number; so, if I can find a quick way to calculate final digit, I'm home free.
Now, let's look for patterns:
6^1 = 6
6^2 = 36
6^3 = 216
hey! Every power of 6 ends in 6.
7^1 = 7
7^2 = 49
7^3 = ...3
7^4 = ...1
9^1 = 9
9^2 = 81
9^3 = ..9
So, putting that into our expression:
(...6) - (...1) - (...9) = (...5) - (...9) = (...6)
choose C!
