Aptitude Day 11

     

Answers of Day 10: 1. 3

                                     2. 1

                                     3. 1

                                     4. 3

                                  

The Cycle of Unit Digit:

  

Today we're gonna look at the cycle of unit digit 8.

     8¹ = 8

     8² = 64

     8³ =512

     8⁴ = 4096

     8⁵ = 32768

     8⁶ = 262144

     8⁷ = 2097152

     8⁸ = 16777216

     8⁹ = 134217728

     8¹⁰ = 1073741824

If you notice the unit digit in all 10, you can see, it repeats. 8,4,2,6 (which I’ve highlighted) then again 8,4,2,6and so on. 

So the cycle of unit digit 8 is

   8¹ = 8 (if you get the remainder as 1)

   8² = 4 (if you get the remainder as 2)

   8³ = 2 (if you get the remainder as 3)

   8⁴ = 6 (if you get the remainder as 0)

Example: Unit digit of the product of   8²¹ * 8⁶¹ * 8⁷¹ =?

Solution:  Power/ 4. Since it has only 4 (8,4,2,1 ) in the cycle and it again repeats...

Power/4= 21/4. You will get the remainder 1 so the unit digit is 8

                61/4. The remainder will be 1 so the unit digit is 8

                71/4. The remainder will be 3 so the unit digit is 2

 8*8= 64, 4*2=8. So the unit digit of this product is 8.

Problems to solve

1.    8²⁵ *8³⁰ *8²¹ *8³⁶ =?

2.    8⁹⁷*8²⁶ *8⁷⁹=? 

3.    8⁹¹ *8⁸²=?

4.    8¹¹*8²² *8³³ =?

Answers are here Aptitude Day 12