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PS 183 (Patterns/Exponents)

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by mattnyc15 » Sat Jan 16, 2016 10:42 am
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So in this problem, I understand the first step: Find the pattern of unit digits for 3 (43 and 33):

3 - power of 1 = 3
3 - power of 2 = 9
3 - power of 3 = 7
3 - power of 4 = 1
REPEAT

Now what I don't understand is getting to the power of 43 and 33.

Without counting, 3 x 11 = 33 so shouldn't the unit digit of 43^33 be 7?
and 4x11 = 44 (power of 4 is unit digit of 1, subtract 1 exponent to get unit digit of 7)

7 + 7 = 14, Unit digit of 4?

What's wrong with my math?
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by [email protected] » Sat Jan 16, 2016 10:54 am
Hi mattnyc15,

The repeating pattern in the math is 4 digits, so....

...with 33^43... the 43rd power is '10 repeating groups of 4' with 3 'left over' --> those 3 digits would be 3, 9, 7...so THAT units digit is 7.

...with 43^33... the 33rd power is '8 repeating groups of 4' with 1 'left over' --> that 1 digit would be 3...so THAT units digit is 3.

7+3 = 10, so the final units digit is 0.

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by Brent@GMATPrepNow » Sat Jan 16, 2016 12:43 pm
If you're interested, we have a free video on finding the units digit of large powers: https://www.gmatprepnow.com/module/gmat- ... video/1031

You can follow that up with a video question to practice with: https://www.gmatprepnow.com/module/gmat- ... video/1032

I also wrote an article on the same topic: https://www.gmatprepnow.com/articles/uni ... big-powers
The article ends with two additional practice questions.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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