[gsnindia]

I Am Starting This New thread to help other and solidfy my own Fundamental In maths

We Will start with some basic Question In maths which Most of us found them difficult to Handle

We will Concentrate mainly on Number System , Fractions and percentage ,Ratio and proportion ,Time Speed, Distance and work, Algebra, Geometry. some of propability and permutation and combination

I Hope will get Support from the best Brain in this forum.

[gsnindia]

Lets take 1st case

When (2)^256 is divided by 17 What is the remainder ?

We Will make is easy by the way of 256= 8 * 32

Hence 2^256 = [[2^8]]^32 mean we can write 2^8 32 times

Now 2^8 = 256 Now 256/17 will give us remainder 1 Hence the remainder of 2^256 is also 1

It looks Complicated initially But if we break it in smaller terms we get the solution

[gsnindia]

Ok Now Ask you One Question

What is the Remainder you get when you divide 5^125 by 124 ?

Please be easy in approach for every one to understand.

[kabir1224]

Originally Posted by gsnindia

Ok Now Ask you One Question

What is the Remainder you get when you divide 5^125 by 124 ?

Please be easy in approach for every one to understand.

The ans is 25. U can have multiple approaches for this ques but the quickest one is that break 5^125 as 5^123x25. Now 5^123= 125^41 which wil give remaindet as 1 hence the ans is 25.

One thing i would like to suggest is that lets share and discuss all the shortcuts available for the main topics of quant bcoz i feel now its the best time to just revise the tips and techniques and learn some good shortcuts you never know what might strike there.

[mr.s.k.abhi]

Originally Posted by gsnindia

Ok Now Ask you One Question

What is the Remainder you get when you divide 5^125 by 124 ?

Please be easy in approach for every one to understand.

the anser is 25..
Sol:- 5^125= 5^2 * 5^123= 5^2 * (5^3)^41

hence wen (5^125)/124 = [5^2 * (125)^41]/124 = 25 * (1)^41 =25.

[gsnindia]

Now lets us try :

16^5 + 2^15 Divisible By:

I am not giving the choice at it will ease the problem , Please give the lucid answers.

[gsnindia]

Originally Posted by kabir1224

One thing i would like to suggest is that lets share and discuss all the shortcuts available for the main topics of quant bcoz i feel now its the best time to just revise the tips and techniques and learn some good shortcuts you never know what might strike there.

That is infact A good idea, We must Start with Final Rivision of the Fundamental

Fundamentral of Number System :

I Understand many people have problem Finding The HCF or LCM

Let me share my learing in Lucid Way.

HCF : It is Nothing but the lowest Powered factor which is Common to all numbers

E.g :
150 : 5*5*3*2
210 :5*2*7*3
375 : 5*5*5*3

here we can easily make out that 5 and 3 is common in all.
hence HCF : 5 * 3 =15
---------------------------------------------------------------
LCM : It is Nothing but the Highest Powered factor of prime No in all, But may Not be Common.

If we have to find the LCM of the Numbers

150 : 5*5*3*2 ==== 5^2 * 3 * 2
210 : 5*2*7*3 ==== 5*2*7*3
375 : 5*5*5*3 ==== 5^3 * 3

Her we can see that max powered no is 5 is 3 --5^3
and 3 is 1
, 2 is 1
, 7 is 1

so the LCM will be : 5^3 *2*3*7 = 5250

remember HCF(N1,N2).LCM(N1,N2) = N1.N2

[gsnindia]

Some Theorems of Divisibility

1. The Highest power of a prime No p is which divide N! exactly is

N/p + N/(p^2) +N/(p^3)+ ..........

Depending Upon the value of N, if N> p^2 then we will have

N/p + N/(p^2)

Let us take an example

What is the Highest power of 3 which will divide 80! ?

Here 3^= 9, 3^3 = 27 , 3^4 = 81 < 80(i.e N)

Here we have

N/p + N/(p^2) +N/(p^3) = 80/3+ 80/9 +80/27 = 26 + 8 + 2 here we take only the Integer < 80/3 (Mean 26.6666 we will take 26 only)

[gsnindia]

Originally Posted by gsnindia

Now lets us try :

16^5 + 2^15 Divisible By:

I am not giving the choice at it will ease the problem , Please give the lucid answers.

The Answer to This Question is As below

we first make them to the power of 2

2^4=16 , hence 2^20 + 2^15 = 2^15(2^5 +1) = 2^15(33) hence it is divisible by 33

[vinnyDpu]

Originally Posted by gsnindia

That is infact A good idea, We must Start with Final Rivision of the Fundamental

Fundamentral of Number System :

I Understand many people have problem Finding The HCF or LCM

Let me share my learing in Lucid Way.

HCF : It is Nothing but the lowest Powered factor which is Common to all numbers

E.g :
150 : 5*5*3*2
210 :5*2*7*3
375 : 5*5*5*3

here we can easily make out that 5 and 3 is common in all.
hence HCF : 5 * 3 =15
---------------------------------------------------------------
LCM : It is Nothing but the Highest Powered factor of prime No in all, But may Not be Common.

If we have to find the LCM of the Numbers

150 : 5*5*3*2 ==== 5^2 * 3 * 2
210 : 5*2*7*3 ==== 5*2*7*3
375 : 5*5*5*3 ==== 5^3 * 3

Her we can see that max powered no is 5 is 3 --5^3
and 3 is 1
, 2 is 1
, 7 is 1

so the LCM will be : 5^3 *2*3*7 = 5250

remember HCF(N1,N2).LCM(N1,N2) = N1.N2

gr8 initiative buddy...!!! I am sure this will help us sharpen our fundas just bfor D-DAY..!!! Happy Dasherra