Aptitude Day 6

Answers of Day 5:   1.  0
                                  2.  4
                                  3.  8
                                  4.  2

The cycle of Unit Digit:
  
Today we're gonna look at the cycle of unit digit 2.

      2¹ = 2

     2² = 4

     2³ = 8

     2⁴ = 16

     2⁵ = 32

     2⁶ = 64

     2⁷ = 128

     2⁸ = 256

     2⁹ = 512

     2¹⁰ = 1024 

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

So the cycle of unit digit 2 is

     2¹ =  2 (if you get the remainder as 1)

    2² =  4 (if you get the remainder as 2)

    2³  =  8 (if you get the remainder as 3)

    2⁴  =  6 (if you get the remainder as 0)

Example: Unit digit of the product of   2³ * 2¹² * 2¹⁷ =?

Solution:  Power/ 4. Since it has only 4 (2,4,8,6) in the cycle and it again repeats 2,4,8,6...

Power/4= 3/4. You will get the remainder 3 so the unit digit is 8

                12/4. The remainder will be 0 so the unit digit is 6

                17/4. The remainder will be 1 so the unit digit is 2

 8*6= 48, 8*2=16. So the unit digit of this product is 6.

Problems to solve

  

1.   2¹⁹ *2³²  *2⁷⁹  =  ?

2.    2¹³ *2²¹ *2¹⁸ *2³⁰  =  ?

3.    2⁷ * 2¹¹ *2⁴⁹ *2⁶⁰  =  ? 

4.    2⁶⁹ * 2⁷³ * 2⁸⁴ *  2¹⁴ * 2⁷⁸   =  ?

Check out the answers here Aptitude Day 7