blackcrow wrote:

If you divide 7^131 by 5, which remainder do you get?

A. 0

B. 1

C. 2

D. 3

E. 4

To determine the remainder when 7^131 is divided by 5, we need only to divide the units digit of 7^131 by 5.

Let’s determine the units digit of 7^131:

When writing out the pattern of 7 raised to positive integer exponents, notice that we are concerned ONLY with the units digit of 7 raised to each power.

7^1 = 7

7^2 = 9

7^3 = 3

7^4 = 1

7^5 = 7

The pattern of the units digits of powers of 7 repeats every 4 exponents. The pattern is 7–9–3–1. In this pattern, we see that all positive exponents that are multiples of 4 will produce a 1 as its units digit. Thus:

7^132 has a units digit of 1 and so 7^131 has units digit of 3. So, the remainder of 3/5 = 3.

Answer: D

_________________

Jeffery Miller

Head of GMAT Instruction

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions