What is the units digit of 18^47 ?

what is the difficulty level of this question?

Since we only care about units digits, the units digit of 18^47 will be the same as the units digit of 8^47.

Let’s determine the units digit of 8^47 by determining 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 a 6 as their units digits. Thus:

8^48 has a units digit of 6.

8^47 has a units digit of 2.

Answer: B

I'd say the difficulty level is ~650.

B) 2

18^47 = (3^47) * (3^47) * (2^47)

Solving for units digit individually, we get unit's digit for 3^47 as 7 and of 2^47 as 8 (as 47/4 has remainder 3). Therefore, 7*7*8 has unit's digit 2.

Hi,

\(18^{47}\), considering the unit digits only,
\(=8^{46}*8\)

\(=4^{23}*8\)

\(=4^{22}*4*8\)

\(=6^{11}*2\)

\(=6*2\)

\(=2\)

Answer (B)

Regards,

Hi,

Just sharing a thought. I haven't managed to understand how the difficulty of the questions is decided - not by you in the GMATCLUB, but by GMAC.

This one for example is very very difficult, if you don't know the simple trick of the cyclicity of the powers. If you do know it however, it becomes ridiculously easy...

So, in fact, it requires very little reasoning and quite a bit of either math knowledge or GMAT tricks knowledge... At least for me, a psychologist that wants to do a psychology PhD in a marketing department that requires the GMAT, I didn't reason at all while solving this one.. Just increased the powers of 8 until the same last digit came up and counted...

The unit digit will be the unit digit of 8x7

That't not correct. It's 18^47, not 18*47.

Whops, yes, my bad!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.