Aptitude Day 7

     

Answers of Day 6: 1. 4

                                2. 4

                                3. 8

                                4. 4

The Cycle of Unit Digit:

  

Today we're gonna look at the cycle of unit digit 3.

     3¹ = 3

     3² = 9

     3³ = 27

     3⁴ = 81

     3⁵ = 243

     3⁶ = 729

     3⁷ = 2187

     3⁸ = 6561   

     3⁹ = 19683

     3¹⁰ = 59049

If you notice the unit digit in all 10, you can see, it repeats. 3,9,7,1 (which I’ve highlighted) then again 3,9,7,1 and so on. 

So the cycle of unit digit 3 is

   3¹ = 3 (if you get the remainder as 1)

   3² = 9 (if you get the remainder as 2)

   3³ = 7 (if you get the remainder as 3)

   3⁴ = 1 (if you get the remainder as 0)

Example: Unit digit of the product of   3³ * 3⁶ * 3⁹ =?

Solution:  Power/ 4. Since it has only 4 (3,9,7,1 ) in the cycle and it again repeats...

Power/4= 3/4. You will get the remainder 3 so the unit digit is 7

                6/4. The remainder will be 2 so the unit digit is 9

                9/4. The remainder will be 1 so the unit digit is 3

 7*9= 63, 3*3=9. So the unit digit of this product is 9.

Problems to solve

1.    3⁸⁴*3²⁵ *3⁷⁶ *3⁶ =?

2.    3⁶³ * 3⁹ *3⁶⁷ *3¹² * 3¹⁹ =? 

3.    3²⁷ * 3³³ * 3⁷⁹ =?

4.    3¹¹ * 3¹⁵ * 3⁹⁰ =?

Answers are here Aptitude Day 8