BTGModeratorVI wrote: ↑Tue Feb 18, 2020 11:02 am
What is the remainder when (2^16)(3^16)(7^16) is divided by 10?
A. 0
B. 2
C. 4
D. 6
E. 8
Source: Veritas
Answer:
D
Key concept: (x^n)(y^n)(z^n) = (xyz)^n
So, we can write: (2^16)(3^16)(7^16) = (2 x 3 x 7)^16
= (42)^16
At this point we need only find the unit's digit of (42)^16
42¹ = 4
2
42² = ---
4
42³ = ---
8
42⁴ = ---
6
42⁵ = ---
2
42 has a cycle of 4 (the units digit repeats every 4 powers)
This means 42^8 = ---
6, 42^12 = ---
6, 42^16 = ---
6, etc
Since 42^16 = ---
6, we can conclude that 42^16, when divided by 10, will leave a remainder of
6
Answer: D
Cheers,
Brent
