What is the units digit of 18^47 ?

Question

A. 0
B. 2
C. 4
D. 6
E. 8

Bunuel · Accepted Answer

The last digit of 18^47 is the same as the last digit of 8^47. 8^1= 8 ; 8^2=6 4 ; 8^3=... 2 ; 8^4=... 6 ; 8^5=...8; ... So the last digit of 8 in power repeats a pattern of 4 numbers: 8-4-2-6 --> 47=11* 4 + 3 , which means that the last digit of 8^47 will be the same as that of 8^3 (the third from the pattern), which is 2. Answer: B. Check Number Theory chapter of Math Book for more: math-number-theory-88376.html Hope it helps.

nusmavrik · Answer

47/4 remainder = 3

18^3. The unit digit is 2. hence answer is B

Desperate123 · Answer

what is the difficulty level of this question?

Bunuel · Answer

I'd say the difficulty level is ~650.

eeshan89 · Answer

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.

cyberjadugar · Answer

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,

pacifist85 · Answer

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...

ugurozturk · Answer

The unit digit will be the unit digit of 8x7

Bunuel · Answer

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

ugurozturk · Answer

Whops, yes, my bad!

ScottTargetTestPrep · Answer

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

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What is the units digit of 18^47 ?

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What is the units digit of 18^47 ?

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