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What is the units digit of [m](3^70)(7^71)[/m]?

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BrentGMATPrepNow
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What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   Updated on: 27 Nov 2021, 09:25
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Question Stats:

81% (00:59) correct 19% (01:03) wrong based on 73 sessions
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What is the units digit of \((3^{50})(7^{52})\)?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Challenge: Can you solve the question in your head?
ShowHide Answer
Official Answer
E

Originally posted by BrentGMATPrepNow on 27 Nov 2021, 08:08.
Last edited by BrentGMATPrepNow on 27 Nov 2021, 09:25, edited 2 times in total.
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   27 Nov 2021, 09:10
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BrentGMATPrepNow wrote:
What is the units digit of \((3^50)(7^52)\)?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Challenge: Can you solve the question in your head?


Hi BrentGMATPrepNow,
Is the question correctly formatted?
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BrentGMATPrepNow
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   27 Nov 2021, 09:16
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errorlogger wrote:
Hi BrentGMATPrepNow,
Is the question correctly formatted?


Oops. I forgot I needed squiggle brackets.
I've corrected the formatting.

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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   27 Nov 2021, 09:20
Cyclcity of 3 : 3,9,7,1
Cyclicity of 7 : 7,9,3,1
3^50 unit digit :9
7^52 unit digit : 1
9*1:9
Option E


BrentGMATPrepNow wrote:
What is the units digit of \((3^{50})(7^{52})\)?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Challenge: Can you solve the question in your head?


Posted from my mobile device
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BrentGMATPrepNow
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   27 Nov 2021, 09:25
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Archit3110 wrote:
Cyclcity of 3 : 3,9,7,1
Cyclicity of 7 : 7,9,3,1
3^50 unit digit :9
7^52 unit digit : 1
9*1:9
Option E

Nice work!
Can you also spot a shortcut that helps us answer the question in 10 seconds?
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   27 Nov 2021, 09:46
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BrentGMATPrepNow
Another way is

3^50*7^50*7^2
For
3^50*7^50 unit digit is 1 and 7^2:unit digit 9
1*9;9 option E

BrentGMATPrepNow wrote:
Archit3110 wrote:
Cyclcity of 3 : 3,9,7,1
Cyclicity of 7 : 7,9,3,1
3^50 unit digit :9
7^52 unit digit : 1
9*1:9
Option E

Nice work!
Can you also spot a shortcut that helps us answer the question in 10 seconds?


Posted from my mobile device
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   27 Nov 2021, 09:59
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BrentGMATPrepNow wrote:
What is the units digit of \((3^{50})(7^{52})\)?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Challenge: Can you solve the question in your head?


Useful property: \((x^k)(y^k) = (xy)^k\)

First rewrite the given expression as follows: \((3^{50})(7^{52})=(3^{50})(7^{50})(7^{2})\)

Apply the property to get: \((3^{50})(7^{50})(7^{2}) = (3 \times 7)^{50}(7^{2}) \)

Evaluate: : \((3 \times 7)^{50}(7^{2})=(21)^{50}(7^{2}) \)

Since \(21^n\) has units digit \(1\) for ANY positive integer \(n\) we can write: \((21)^{50}(7^{2}) = (????1)(49) =\) ?????9

Answer: E
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink] New post   14 Jun 2023, 03:22
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
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