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18 May 2020, 01:30
Kudos
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Units digit is a rather easy concept but has a tricky approach on the GMAT questions!!
Well, let’s understand it!
Units digit is the rightmost digit of a number.
For example units digit of 356 is 6
units digit of 2347543 is 3 ……Quite Easy!!
Units digit of 3412*5439 would be the same as the units digit of 2*9, as only the units digits of the larger numbers are considered in such a calculation. 2*9 = 18, so the unit digit of 3412*5439 is 8….Yep Easy!!
Finding the units digit of 2322^2322 is not straightforward.....
Let’s learn the technique to calculate the units digit of such large numbers in a few seconds
Units digit of 〖2322〗^2322
Step 1: Identify the unit digit of Base, in our example, it is (2)
Step 2: Identify the last 2 digits of Power, in our example it is (22)
Step 3: Now divide the last two digits of the power by 4, that is (22/4) and find the remainder which is 2 here
Step 4: Find (unit digit of Base^ Remainder obtained in step 3) in our example it is 2^2=4. Which is hence the units digit asked in our question.
Note: But there is an exception to this rule in step 4
When the remainder is zero:
Find (unit digit of Base^4), which is then units digit asked in our question.
Let’s apply this on gmat question
What is the units digit of (2222^333) *(3333^220)
A. 0
B. 2
C. 4
D. 6
E. 8
Units digit of (2222^333) *(3333^220) is the same as unit digit of (2^333) *(3^220)
To find the Unit digit of (2222^333)
Unit digit of the base is 2
Last 2 digits of power is 33
Divide 33 by 4 where the remainder is 1
Now, (2^1) =2, is the unit digit of (2222^333)
To find the Unit digit of (3333^220)
[b]Unit digit of the base is 3
Last 2 digits of power is 20
Divide 20 by 4, where the remainder is 0
Following the Exception,
(3^4) = (3^2*3^2)
9 *9 =1, is the unit digit of (3333^220)
Thus, the unit digit of (2222^333) *(3333^220) is (2*1) =2
Cheers!!
Manisha
Gmat quant Expert and Instructor
PrepMinds - Founder
Well, let’s understand it!
Units digit is the rightmost digit of a number.
For example units digit of 356 is 6
units digit of 2347543 is 3 ……Quite Easy!!
Units digit of 3412*5439 would be the same as the units digit of 2*9, as only the units digits of the larger numbers are considered in such a calculation. 2*9 = 18, so the unit digit of 3412*5439 is 8….Yep Easy!!
Finding the units digit of 2322^2322 is not straightforward.....
Let’s learn the technique to calculate the units digit of such large numbers in a few seconds
Units digit of 〖2322〗^2322
Step 1: Identify the unit digit of Base, in our example, it is (2)
Step 2: Identify the last 2 digits of Power, in our example it is (22)
Step 3: Now divide the last two digits of the power by 4, that is (22/4) and find the remainder which is 2 here
Step 4: Find (unit digit of Base^ Remainder obtained in step 3) in our example it is 2^2=4. Which is hence the units digit asked in our question.
Note: But there is an exception to this rule in step 4
When the remainder is zero:
Find (unit digit of Base^4), which is then units digit asked in our question.
Let’s apply this on gmat question
What is the units digit of (2222^333) *(3333^220)
A. 0
B. 2
C. 4
D. 6
E. 8
Units digit of (2222^333) *(3333^220) is the same as unit digit of (2^333) *(3^220)
To find the Unit digit of (2222^333)
Unit digit of the base is 2
Last 2 digits of power is 33
Divide 33 by 4 where the remainder is 1
Now, (2^1) =2, is the unit digit of (2222^333)
To find the Unit digit of (3333^220)
[b]Unit digit of the base is 3
Last 2 digits of power is 20
Divide 20 by 4, where the remainder is 0
Following the Exception,
(3^4) = (3^2*3^2)
9 *9 =1, is the unit digit of (3333^220)
Thus, the unit digit of (2222^333) *(3333^220) is (2*1) =2
Cheers!!
Manisha
Gmat quant Expert and Instructor
PrepMinds - Founder
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