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Units digit of n^33 is 7

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Units digit of n^33 is 7

by vivibcn » Sun Oct 21, 2012 5:47 am
Could you please explain how to solve the following?

If the units digit of n^33 is 7, which of the following could be the value of n?

I. n =41
II. n = 43
III. n = 47

a. Only I
b. Only II
c. Only III
d. I and II
e. II and III
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by teejaycrown » Sun Oct 21, 2012 7:04 pm
This is a pattern problem. If 41 is raised to the power of 33, the unit digits will remain 1 for any power. 41^1 = 41' 41 ^2 =.....1, 41^10 = .....1
For 43 , the pattern for the power will be 43^1= 43, 43 ^ 2 = ....9, power 3 units digit 7 from 27, power 4 unit digit = 1. From this, the pattern is 3,9,7,1,3,9,7,1. The pattern repeats itself every 4th power. Therefore, 43^32 will have 1 as a unit digit since 32 is a multiple of 4 while 43^33 will have a unit digit of 3 and not 7.

For the last option 47, the pattern is 7,9,3 and 1 and this repeats itself every 4th power. Therefore, 43^32 has 1 has unit digit while 43^33 has 7 has unit digit.

The answer is option III only.

I m also preparing for GMAT and I have received tremendous help from experts on this forum. Rgds
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