amgelcer wrote:

What is the units digit of the expression 14^7−18^4?

(A) 0

(B) 3

(C) 4

(D) 6

(E) 8

Since we only care about units digits, we can rewrite the expression as:

4^7 − 8^4

Let’s start by evaluating the pattern of the units digits of 4^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 4. When writing out the pattern, notice that we are ONLY concerned with the units digit of 4 raised to each power.

4^1 =

4 4^2 =

6 4^3 =

4 4^4 =

6 The pattern of the units digit of powers of 4 repeats every 2 exponents. The pattern is 4–6. In this pattern, all positive exponents that are odd will produce a 4 as its units digit. Thus:

4^7 has a units digit of 4.

Next, we can evaluate the pattern of the units digits of 8^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 8. When writing out the pattern, notice that we are ONLY concerned with the units digit of 8 raised to each power.

8^1 =

8 8^2 =

4 8^3 =

2 8^4 =

6 8^5 =

8 The pattern of the units digit of powers of 8 repeats every 4 exponents. The pattern is 8–4–2–6. In this pattern, all positive exponents that are multiples of 4 will produce an 8 as its units digit. Thus:

8^4 has a units digit of 6.

Thus, the “units digit” of 4^7 − 8^4 is 4 − 6 = –2. However, we can’t have a negative number as the unit digit. When we encounter such a case, we add 10 to make it positive. Thus, the the units digit of 4^7 − 8^4 is –2 + 10 = 8.

Answer: E

_________________

Scott Woodbury-Stewart

Founder and CEO

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions