supreetb wrote:

Find the ones digit of 73^350

A) 3

B) 5

C) 6

D) 7

E) 9

Since we only care about units digits, we really are determining the units digit of 3^350.

Let’s evaluate the units digit of 3^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 3. When writing out the pattern, notice that we are ONLY concerned with the units digit of 3 raised to a power.

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

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

3^348 has a units digit of 1 and 3^349 has a units digit of 3, and thus 3^350 has a units digit of 9.

Answer: E

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Jeffery Miller

Head of GMAT Instruction

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