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# What is the units digit of 7^20?

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

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03 Feb 2017, 02:07
00:00

Difficulty:

15% (low)

Question Stats:

68% (00:26) correct 32% (00:24) wrong based on 94 sessions

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

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 07 Mar 2015 Posts: 110 Location: India Concentration: General Management, Operations GMAT 1: 590 Q46 V25 GPA: 3.84 WE: Engineering (Energy and Utilities) Re: What is the units digit of 7^20? [#permalink] ### Show Tags 03 Feb 2017, 02:27 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... Senior Manager Joined: 23 Feb 2015 Posts: 430 Re: What is the units digit of 7^20? [#permalink] ### Show Tags 03 Feb 2017, 02:39 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 $$7^2^0$$ _________________ “The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5610 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: What is the units digit of 7^20? [#permalink] ### Show Tags 05 Feb 2017, 18:53 ==> 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. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: What is the units digit of 7^20? [#permalink]

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05 Feb 2017, 23:24
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, 02:51
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
Math Expert
Joined: 02 Sep 2009
Posts: 46335
Re: What is the units digit of 7^20? [#permalink]

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07 Feb 2017, 05:00
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, 07:38
$$7^4$$ = $$7*7*7*7$$= $$49*49$$ = 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
Posts: 41
Re: What is the units digit of 7^20? [#permalink]

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07 Feb 2017, 10:41
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, 19:45
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.

Answer: A
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Re: What is the units digit of 7^20?   [#permalink] 08 Feb 2017, 19:45
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# What is the units digit of 7^20?

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