UNITS DIGITS – 1

It is common to get 1 or 2 unit digit question in GMAT. However, it is also utilized in other question such as one where we are testing divisibility.

The unit digit of any expression can be obtained by using only the unit digit of each number involved in the expression. Hence rather than solving the complete equation to retrieve the unit digit, always focus on the unit digit of the given numbers.

For eg.

To find the unit digit of (223 * 3456), we don’t need to solve the complete expression 223 * 3456 instead we can multiply 3(unit digit of 223) and 6 (unit digit of 3456) to get the unit digit of expression i.e. 8 in this case.

 

Let’s understand some unit digit cycle that we get once we keep increasing the degree of a given number –

Unit degree cycle for 0 ->

Any degree of 1 will always give 1 as a unit digit

 

Unit degree cycle for 1 ->

Any degree of 1 will always give 1 as a unit digit

 

Unit degree cycle for 2 –>

1st degree of 2 -> 2

2nd degree of 2 -> 2 * 2 -> 4

3th degree of 2 -> 4 * 2 -> 8

4th degree of 2 -> 8 * 2 -> 6

5th degree of 2 -> 6 * 2 -> 2

At 5th degree we will start repeating the unit digit similar to 1st digit. Hence we can represent the unit digit cycle of 2 is 4.

5st degree of 2 = (4n + 1) degree of 2

= (Unit digit of 1st degree of 2) = 2

6th degree of 2 = (4n + 2) degree of 2

= (Unit digit of 2st degree of 2) = 2 * 2 = 4

7th degree of 2 = (4n + 3) degree of 2

= (Unit digit of 3st degree of 2) = 2 * 2 * 2 = 8

8th degree of 2 = (4n + 4) degree of 2

= (Unit digit of 4th degree of 2) = 2 * 2 * 2 * 2 = 6

9th degree of 2 = (4n + 1) degree of 2

= (Unit digit of 1st degree of 2) = 2

 

Similarly the unit digit for other number can be found.

Unit degree cycle for 3 ->

Unit degree cycle for 4 ->

Unit degree cycle for 5 -> Any degree of 5 will always result in 5.

Unit degree cycle for 6 -> Any degree of 6 will always result in 6.

Unit degree cycle for 7 ->

Unit degree cycle for 8 ->

Unit degree cycle for 9 ->

NOTE – You don’t need to memorize these cycle, you can create one as and when you need.

 

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