Hey puys, As we all are geared up to prepare ALL NEW CAT 2014, let us refresh our quant concepts bit by bit. All we need to do is just mention the topic name followed by the concept and illustrate it with an example or two. So, let’s get started…
Hey puys, As we all are geared up to prepare ALL NEW CAT 2014, let us refresh our quant concepts bit by bit. All we need to do is just mention the topic name followed by the concept and illustrate it with an example or two. So, let's get started...
1) Remainders (Numbers)
To find the remainder when dividend is of the form (a^n + b^n) or (a^n - b^n)
case 1) (a^n + b^n) is divisible by (a+b) when n is ODD
case 2) (a^n - b^n) is divisible by (a+b) when n is EVEN
case 3) (a^n - b^n) is ALWAYS divisible by (a-b)
Ex: 1) Find the remainder when (3^444 + 4^333) is divided by 5?
This can be written as (3^4)^111 + (4^3)^111. As 111 is ODD the expression is divisible by (a+b) i.e., (3^4 + 4^3) = 145
Since the number is divisible by 45, it is definitely divisible by 5. Therefore the remainder is zero
Hope you guys come up with new concepts so that we never miss the track of fundaes...
2) Concept : To Find the smallest number that leaves a specific remainder r when divided by a,b,c..
The funda here is to take lcm of a,b and c...and add r to it.
Ex: find Smallest no, that leaves remainder 3 when divided by 5,6,8 or 9.
LCM of 5,6 8 and 9 is 360, add 3 to it
363 is the answer
Am starting with easier concepts..let us build it as we go ahead..
I would appreciate if puys contribute actively towards revising the concepts @sagarcat @shawshanks @Highway66 @dipayan22@jay3421 @rgvcat_2013 @prate3k @swapnil4ever2u @neorevlutn @guptaashima4143 ..post a concept...
I learnt it somewhere , wanted to share it :
example 1 => trick for a
number of ways in which 5 numbers or n numbers can be selected from 1 to 9 , such that a
is 13C5
solution :
a will always be less than b+1
b will always be less than C+1
c
in short ,
a
as max value is 9 , so , e+4 can be 9+4 = 13 maximum
in short , select any 5 numbers from 1 to 13 viz 13C5 😃
No of squares in a board of dimension m*n where m=n-a and a>=0. Is summation m( m+a). No of rectangle is summation m * summation n.
a^m-1; a^n-1
HCF is a^HCF(m,n)-1
if three altitudes lets say h1,h2,h3 are given then area of triangle is,,, root[(a+b+c)(-a+b+c)(a-b+c)(a+b-c)] where a=1/h1 b=1/h2,,c=1/h3
All composite numbers satisfy the condition that (n-1)! is divisible by n except 4 .
Concept for the day:
Let N be a composite number such that N=(x)^a*(y)^b*(z)^c where x, y, z are prime factors. Then the number of divisors of N=(a+1)(b+1)(c+1)
Ex: Find the number of divisors of of 60
60 = 2^2*3*5
Here power of 2 contains 2^0, 2^1 and 2^2, power of 3 contains 3^0 and 3^1 and power of 5 contains 5^0 and 5^1.
So, increase the powers of all prime numbers by 1 and multiply them to get total number of divisors.
In this case,
Number of divisors = (2+1)(1+1)(1+1) = 12
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days canA do the work if he is assisted by B and C on every third day?
P beats Q by 125 m in a kilometer race. Find Q's speed if P's speed is 16 m/s
FIBONACCI NUMBERS
let Un be the nth fibonacci number then
1) U(n-1) + U(n-2) = Un
2) (Un)^2 + ( U(n+1) )^2 = U(2n+1)
3) (Un)^2 - ( U(n-2) )^2 = U(2n-2)
4) (Un)^2 - ( U(n-1) )^2 = U(n-2) * U(n+1)
5) summation (Un)^2 =Un * U(n+1)
6 summation Un = U(n+2) - 1
Today's concept: TSD
Two bodies start from opposite ends A & B at the same time and move towards each other with speed S1 and S2. After meeting each other, they take T1 and T2 to reach their destinations. The relation is given by,
S1/S2 = √(T2/T1)
Time taken for the bodies to meet will be
T = √(T1*T2)
Last digit of 2^3^4^5??
Concept for the day: Algebra:
The roots of the quadratic eqn ax^2+bx+c=0 is
{-b±√(b^2-4ac)}/2a.
The co-efficient of x^2 decides whether the eqn has maxima or minima.
If the co-efficient is +ve then, eqn will have minima and
if the co-efficient is -ve then, eqn will have maxima.
The maxima/minima occurs at x=-b/2a
The maximum/minimum value the expression can take is
(4ac-b^2)/4a
Guys, what kind of questions appear in CAT under the "Pigeon hole principle"??
Number of ways of distributing 'r' non distinct objects into 'n' distinct cells with each cell containing at least 'q' number of objects, provided (r>=n) is C (n-nq+r-1,n-1)
2 cards r drawn from a well shuffled pack f cards given both cards r numbered what is d prob that the cards have same no but diff colours on them..