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The units digit of [(137^13)^47] is which of the following

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by Mike@Magoosh » Tue Aug 20, 2013 12:37 pm
The units digit of [(137^13)^47] is which of the following?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

[spoiler]OA: (B)[/spoiler]

This is a very hard units digit question, probably a notch harder than anything you will see on the GMAT. For a complete discussion of units digit questions, as well as a full solution to this particular question, see:
https://magoosh.com/gmat/2013/gmat-quant ... questions/

Experts, would you like to share any further resources about units digit questions?

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by srijoyray » Tue Aug 20, 2013 7:03 pm
Great sum. Thanks for sharing.

My thought process: 13 * 47 = 611. 611 divided by 4 leaves a remainder 3.

7^3 = 343
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by ganeshrkamath » Tue Aug 20, 2013 8:24 pm
Mike@Magoosh wrote:The units digit of [(137^13)^47] is which of the following?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

[spoiler]OA: (B)[/spoiler]

This is a very hard units digit question, probably a notch harder than anything you will see on the GMAT. For a complete discussion of units digit questions, as well as a full solution to this particular question, see:
https://magoosh.com/gmat/2013/gmat-quant ... questions/

Experts, would you like to share any further resources about units digit questions?

Mike :-)
Power of 7 have units digit cycling through 7,9,3,1.
i.e.
7^1 => 7
7^2 => _9
7^3 => __3
7^4 => ___1
7^5 => ___7
and so on

137^13 = 137^12 * 137^1 = (137^4)^3 * 137^1 = 1^3 * 7 = 7

Again 7^47 = 7^44 * 7^3 = (7^4)^11 * 7^3 = 1 * 3

So the units digit of (137^13)^47 is 3.
Choose B

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