Problem Solving

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 = 42
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