CAT Lessons--Quantitative Aptitude
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Targeting High marks in CAT,Improve your Quant.....

Numbers
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In last post we discussed about finding unit digit of a large power using Fermat's theorem and co-prime Technique.Now move 1 step forward,Find last 2 digits.
To find tens digit or last two digits, we will follow the same techniques except for this time we will divide by 100. 100 has 40 relative primes.
100(1-1/2)(1-1/5)=40

So to find tens digit of 69^83 we will divide 83 by 40 [power by relative primes]. We will get 3 as remainder. So we are left with 69^3 divided by 100.
this can be done manually by multiplying only the last 2 digits.
we will get 69.

Similarly we can do it for last three digits, method remains same but this time we will divide by 1000.
also remember,no. of co-primes for 1000=1000(1-1/2)(1-1/5)=400


Some examples are given
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* “What will be the remainder when 68^66 is divided by 5”.

First find relative primes of 5 [ 5 is prime so its relative primes are 4]
Now divide the power of 68^66 by 4, so we get 2.
Now we are left with 68^2 divided by 5.
Do 8^2/5, will get remainder as 4.

Suppose the base of numerator and denominator are not relative primes then take out the relative prime from Nr and Dr and multiply it in the end.


*Find the remainder when 78^67 is divided by 8.

Here we take out 2 from base of Nr and Dr. Hence we are left with
2*{39^67/4}.
Applying our usual method to get remainder as 3 multiplying with 2 to get the result as 6.


More posts on quant and DI are coming soon......

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