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What is the units digit of 7^20?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4897
GPA: 3.82
What is the units digit of 7^20? [#permalink]

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03 Feb 2017, 01:07
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Difficulty:

15% (low)

Question Stats:

69% (00:26) correct 31% (00:23) wrong based on 90 sessions

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What is the units digit of $$7^{20}$$?

A. 1
B. 3
C. 5
D. 7
E. 9
[Reveal] Spoiler: OA

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Re: What is the units digit of 7^20? [#permalink]

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03 Feb 2017, 01:27
MathRevolution wrote:
What is the units digit of $$7^2^0$$?

A. 1
B. 3
C. 5
D. 7
E. 9

Power cycle of 7 -- 7 ,9,3,1

so it should be 1...
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Re: What is the units digit of 7^20? [#permalink]

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03 Feb 2017, 01:39
MathRevolution wrote:
What is the units digit of $$7^2^0$$?

A. 1
B. 3
C. 5
D. 7
E. 9

The cyclicity of 7 is 4. So, 20/4 gives us the unit digit 1 of $$7^2^0$$
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Joined: 16 Aug 2015
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GPA: 3.82
Re: What is the units digit of 7^20? [#permalink]

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05 Feb 2017, 17:53
==> Since $$~7^1=~7, ~7^2=~9, ~7^3=~3, ~7^4=~1$$, the exponent has a cycle of four, which makes 20=4*5. Then, $$7^2^0=(7^4)^5=~1$$ is derived and the answer is A.
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Joined: 14 Nov 2014
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Re: What is the units digit of 7^20? [#permalink]

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05 Feb 2017, 22:24
MathRevolution wrote:
What is the units digit of $$7^2^0$$?

A. 1
B. 3
C. 5
D. 7
E. 9

to reduce the calculation little ..
I rewritten it as (49)^10
for 9 , we know unit digit is 9,1,9,1..
so 1.
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Re: What is the units digit of 7^20? [#permalink]

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07 Feb 2017, 01:51
MathRevolution wrote:
What is the units digit of $$7^2^0$$?

A. 1
B. 3
C. 5
D. 7
E. 9

The question asks 7^2^0 not 7^20.

If it was 7^20, then yes the units digit would be 1. But 7^2^0 is equal to 7. The answer should be 7. I think there is something incorrect here, Bunuel and bb
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Joined: 02 Sep 2009
Posts: 43853
Re: What is the units digit of 7^20? [#permalink]

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07 Feb 2017, 04:00
rishit1080 wrote:
MathRevolution wrote:
What is the units digit of $$7^2^0$$?

A. 1
B. 3
C. 5
D. 7
E. 9

The question asks 7^2^0 not 7^20.

If it was 7^20, then yes the units digit would be 1. But 7^2^0 is equal to 7. The answer should be 7. I think there is something incorrect here, Bunuel and bb

It's 7^20. It was just formatted incorrectly. Edited.
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Re: What is the units digit of 7^20? [#permalink]

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07 Feb 2017, 06:38
$$7^4$$ = $$7*7*7*7$$= $$49*49$$ = unit digit $$1$$

$$7^{20}$$ = $$7^4$$ * $$7^4$$ * $$7^4$$ * $$7^4$$ * $$7^4$$ = $$1 * 1 * 1 * 1$$ = unit digit $$1$$
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Joined: 04 Apr 2015
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Re: What is the units digit of 7^20? [#permalink]

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07 Feb 2017, 09:41
Bunuel wrote:
rishit1080 wrote:
MathRevolution wrote:
What is the units digit of $$7^2^0$$?

A. 1
B. 3
C. 5
D. 7
E. 9

The question asks 7^2^0 not 7^20.

If it was 7^20, then yes the units digit would be 1. But 7^2^0 is equal to 7. The answer should be 7. I think there is something incorrect here, Bunuel and bb

It's 7^20. It was just formatted incorrectly. Edited.

7 has cyclicity of 4 so when power 20 divided by 4 gives remainder 0. shouldn't it be 7 as answer. can you explain how remainder is related to cyclicity. where am i missing the link?
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Re: What is the units digit of 7^20? [#permalink]

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08 Feb 2017, 18:45
MathRevolution wrote:
What is the units digit of $$7^{20}$$?

A. 1
B. 3
C. 5
D. 7
E. 9

Let’s start by evaluating the pattern of the units digits of 7^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 7. When writing out the pattern, notice that we are ONLY concerned with the units digit of 7 raised to each power.

7^1 = 7

7^2 = 9

7^3 = 3

7^4 = 1

7^5 = 7

We can see that the pattern of the units digit of powers of 7 repeats every 4 exponents. The pattern is 7–9–3–1. In this pattern, all positive exponents that are multiples of 4 will produce a 1 as its units digit. Thus:

7^20 has a units digit of 1.

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Re: What is the units digit of 7^20?   [#permalink] 08 Feb 2017, 18:45
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