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Units digit?

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oquiella Master | Next Rank: 500 Posts Default Avatar
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Units digit?

Post Mon Sep 28, 2015 2:27 pm
If N=(33)^43 + (43)^33, what is the units digit of n?

A. 0
B. 2
C. 4
D. 6
E. 8

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GMAT/MBA Expert

Post Mon Sep 28, 2015 3:17 pm
FYI - we have a free video on finding the Units Digit of Large Powers -http://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1031

Then you can practice with this question - http://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1032

Cheers,
Brent

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GMAT/MBA Expert

Post Mon Sep 28, 2015 2:35 pm
oquiella wrote:
If N=(33)^43 + (43)^33, what is the units digit of n?

A. 0
B. 2
C. 4
D. 6
E. 8
3¹ --> units digit of 3.
3² --> units digit of 9. (Since the product of the preceding units digit and 3 = 3*3 = 9.)
3³ --> units digit of 7. (Since the product of the preceding units digit and 3 = 9*3 = 27.)
3⁴ --> units digit of 1. (Since the product of the preceding units digit and 3 = 7*3 = 21.)
From here, the units digits will repeat in the same pattern: 3, 9, 7, 1.
The units digits repeat in a CYCLE OF 4.
Implication:
When an integer with a units digit of 3 is raised to a power that is a multiple of 4, the units digit will be 1.

Thus:
33⁴⁰ and 43³² each have a units digit of 1.
From here, the cycle of units digits will repeat: 3, 9, 7, 1...
Thus:
33⁴¹ and 43³³ each have a units digit of 3.
33⁴² has a units digit of 9.
33⁴³ has a units digit of 7.

Result:
Since n = 33⁴³ + 43³³, n ---> (units digit of 3) + (units digit of 7) = units digit of 0.

The correct answer is A.

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Last edited by GMATGuruNY on Sun Jan 07, 2018 4:16 am; edited 1 time in total

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