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Which of the following could be the units digit of where n i

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Which of the following could be the units digit of where n i [#permalink] New post 11 Sep 2017, 16:13
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Which of the following could be the units digit of \(57^n\), where n is a positive integer?

Indicate all such digits.

A) 0
B) 1
C) 2
D) 3
E) 4
F) 5
G) 6
H) 7
I) 8
J) 9



Practice Questions
Question: 4
Page: 123
Difficulty: hard
[Reveal] Spoiler: OA

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Re: Which of the following could be the units digit of where n i [#permalink] New post 11 Sep 2017, 16:21
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Explanation

\(57^n\) is the same as \(7^n\) for the unit digit we care about.

Of course, 7 raised to a power has a repeating pattern

\(7^1=7\)
\(7^2=49\) unit digit is 9
\(7^3=343\) unit digit is 3
.........
up to \(7^9\)

The only answer are B,D,H and J
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Re: Which of the following could be the units digit of where n i [#permalink] New post 01 May 2019, 05:07
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Carcass wrote:
Which of the following could be the units digit of \(57^n\), where n is a positive integer?

Indicate all such digits.

A) 0
B) 1
C) 2
D) 3
E) 4
F) 5
G) 6
H) 7
I) 8
J) 9



Practice Questions
Question: 4
Page: 123
Difficulty: hard


Let’s begin by looking for a pattern as we increase the exponent.

57^1 = 57 (units digit is 7)

57^2 = 3249 (units digit is 9)

Aside: As you can see, the powers increase quickly! So, it’s helpful to observe that we need only consider the units digit when evaluating large powers.
For example, the units digit of 57^2 is the same as the units digit of 7^2, the units digit of 57^5 is the same as the units digit of 7^5, and so on.

Continuing along, we get:

57^3 = (57)(57^2) = (57)(---9) = ----3

57^4 = (57)(57^3) = (57)(---3) = ----1

57^5 = (57)(57^4) = (57)(---1) = ----7

Notice that a nice pattern emerges. We get: 7-9-3-1-7-9-3-1-...

As you can see, the pattern repeats itself every 4 powers.

So, the only possible units digits are 7, 9, 3 and 1

Answer: B, D, H, I

Cheers,
Brent
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Re: Which of the following could be the units digit of where n i   [#permalink] 01 May 2019, 05:07
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