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

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Founder
Joined: 18 Apr 2015
Posts: 6915
Followers: 114

Kudos [?]: 1343 [0], given: 6317

Which of the following could be the units digit of where n i [#permalink]  11 Sep 2017, 16:13
Expert's post
00:00

Question Stats:

84% (00:20) correct 15% (00:14) wrong based on 19 sessions
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

_________________
Founder
Joined: 18 Apr 2015
Posts: 6915
Followers: 114

Kudos [?]: 1343 [1] , given: 6317

Re: Which of the following could be the units digit of where n i [#permalink]  11 Sep 2017, 16:21
1
KUDOS
Expert's post
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
_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 1981
Followers: 60

Kudos [?]: 1803 [1] , given: 9

Re: Which of the following could be the units digit of where n i [#permalink]  01 May 2019, 05:07
1
KUDOS
Expert's post
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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

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