What is the units digit of

BTGmoderatorDC wrote: ↑

Fri Apr 03, 2020 5:24 pm

\(What\ is\ the\ units\ digit\ of\ 15^9\ -\ 16^6?\)

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


OA E

Source: Veritas Prep

If k is a positive integer, then the units digit of 15^k is always 5 (15^1 = 15, 15^2 = 225, 15^3 = 3375, 15^4 = ----5, etc)

If j is a positive integer, then the units digit of 16^j is always 6 (16^1 = 16, 16^2 = 256, 16^3 = 4096, 16^4 = ----6, etc)

So, 15^9 - 16^6 = (----5) - (---6) = ----9

Answer: E

Cheers,
Brent

BTGmoderatorDC wrote: ↑

Fri Apr 03, 2020 5:24 pm

\(What\ is\ the\ units\ digit\ of\ 15^9\ -\ 16^6?\)

(A) 1

(B) 3

(C) 5

(D) 7

(E) 9


OA E

Source: Veritas Prep

The units digit of 15^9 is equal to the units digit of 5^9. Recall that when 5 is raised to any positive integer power, the units digit of the number will always be 5. Similarly, when 16 (or, equivalently, 6) is raised to any positive integer power, the units digit of the number will always be 6.

15^9 has a units digit of 5, and 16^6 has a units digit of 6, so the units digit of 15^9 - 16^6 is 5 - 6 + 10 = 9 (notice that 5 - 6 = -1, but the units digit can’t be negative; since 15^9 is greater than 16^6, we can borrow a “1” from the tens digit of 15^9, i.e., adding a 10 to -1).

Answer: E