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# What is the units digit of 18^47 ?

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What is the units digit of 18^47 ? [#permalink]

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21 Oct 2010, 17:40
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Difficulty:

25% (medium)

Question Stats:

65% (01:37) correct 35% (00:46) wrong based on 348 sessions

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What is the units digit of 18^47 ?

A. 0
B. 2
C. 4
D. 6
E. 8
[Reveal] Spoiler: OA

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21 Oct 2010, 18:03
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Expert's post
shrive555 wrote:
What is the units digit of 18^47 ? (18 power 47 )

0
2
4
6
8

The last digit of 18^47 is the same as the last digit of 8^47.

8^1=8;
8^2=64;
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.

Check Number Theory chapter of Math Book for more: math-number-theory-88376.html

Hope it helps.
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21 Oct 2010, 18:38
47/4 remainder = 3

18^3. The unit digit is 2. hence answer is B
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13 Jul 2012, 11:18
what is the difficulty level of this question?
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14 Jul 2012, 04:03
Desperate123 wrote:
what is the difficulty level of this question?

I'd say the difficulty level is ~650.
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Re: What is the units digit of 18^47 ? [#permalink]

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25 Jul 2012, 02:35
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.
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Re: What is the units digit of 18^47 ? [#permalink]

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25 Jul 2012, 21:38
Hi,

$$18^{47}$$, considering the unit digits only,
$$=8^{46}*8$$

$$=4^{23}*8$$

$$=4^{22}*4*8$$

$$=6^{11}*2$$

$$=6*2$$

$$=2$$

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Re: What is the units digit of 18^47 ? [#permalink]

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10 Dec 2014, 13:46
Hello from the GMAT Club BumpBot!

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Re: What is the units digit of 18^47 ? [#permalink]

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06 Jan 2015, 03:44
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...
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Re: What is the units digit of 18^47 ? [#permalink]

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19 Jan 2015, 06:23
The unit digit will be the unit digit of 8x7
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Re: What is the units digit of 18^47 ? [#permalink]

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19 Jan 2015, 06:27
ugurozturk wrote:
The unit digit will be the unit digit of 8x7

That't not correct. It's 18^47, not 18*47.
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Re: What is the units digit of 18^47 ? [#permalink]

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19 Jan 2015, 06:28
Bunuel wrote:
ugurozturk wrote:
The unit digit will be the unit digit of 8x7

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

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Re: What is the units digit of 18^47 ? [#permalink]

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13 Jan 2017, 04:30
Hello from the GMAT Club BumpBot!

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Re: What is the units digit of 18^47 ? [#permalink]

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16 Jan 2017, 18:09
shrive555 wrote:
What is the units digit of 18^47 ?

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

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.

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Re: What is the units digit of 18^47 ?   [#permalink] 16 Jan 2017, 18:09
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