Aptitude Day 10

     

Answers of Day 9:      1. 6

                                     2. 5

                                     3. 0

                                     4. 0

                                     5. 6

The Cycle of Unit Digit:

  

Today we're gonna look at the cycle of unit digit 7.

     7¹ = 7

     7² = 49

     7³ = 343

     7⁴ = 2401

     7⁵ = 16807

     7⁶ = 117649

     7⁷ = 823543

     7⁸ = 5764801

     7⁹ =40353607

     7¹⁰ =282475249

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

So the cycle of unit digit 7 is

    7¹ = 7 (if you get the remainder as 1)

   7² = 9 (if you get the remainder as 2)

   7³ = 3 (if you get the remainder as 3)

   7⁴ = 1 (if you get the remainder as 0)

Example: Unit digit of the product of   7²⁶ * 7³¹ * 7⁹¹ =?

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

Power/4= 26/4. You will get the remainder 2 so the unit digit is 9

                31/4. The remainder will be 3 so the unit digit is 3

                91/4. The remainder will be 3 so the unit digit is 3

 9*3= 27, 7*3=21. So the unit digit of this product is 1.

Problems to solve

1.    7⁸⁰*7³³ *7⁴⁶ =?

2.    7¹¹*7⁹  =? 

3.    7¹³* 7¹⁹ * 7⁴⁹ * 7⁵¹ =?

4.    7⁶⁴*7¹⁸ *7⁸¹ =?

Answers are here Aptitude Day 11