CAT formulae
14/09/2013
Important Formulae_for website_for CAT2012 students
RATIO – PROPORTION – VARIATION
1. If a : b : : c : d, then ad = bc
2. If a : b : : c : d, then a + b : b : : c + d : d
3. If a : b : : c : d, then a - b : b : : c - d : d
4. If a : b : : c : d, then a + b : a - b : : c + d : c - d
5. If
then k =
NUMBERS
1. a 3 + b 3 + c3 – 3abc = (a + b + c) (a 2 + b 2 + c2 – ab – bc – ca)
2. The product of n consecutive integers is always divisible by n! (n factorial)
3. The sum of any number of even numbers is always even
4. The sum of even number of odd numbers is always even
5. The sum of odd number of odd numbers is always odd
6. If N is a composite number such that N = a p . b q . cr .... where a, b, c are prime factors of N and p, q, r
.... are positive integers, then
a) the number of factors of N is given by the expression (p + 1) (q + 1) (r + 1) ...
b) it can be expressed as the product of two factors in 1/2 {(p + 1) (q + 1) (r + 1).....} ways
c) if N is a perfect square, it can be expressed
(i) as a product of two DIFFERENT factors in 1/2 {(p + 1) (q + 1) (r + 1) ... -1 } ways
(ii) as a product of two factors in 1/2 {(p + 1) (q + 1) (r + 1) ... +1} ways
d) sum of all factors of N =
e) it can be expressed as a product of two co-primes in 2n–1 ways, where ‘n’ is the number of different prime factors of the given number N
time4education.com/CAT_Important_formulaes/CAT_Important_Formulae.asp
1/11
14/09/2013
Important Formulae_for website_for CAT2012 students
f) the number of co-primes of N (< N), f (N) =
g) sum of the numbers in (e) =
SIMPLE INTEREST AND COMPOUND INTEREST
I = Interest, P is Principle, A = Amount, n = number of years, r is rate of interest
1. Interest under
a) Simple interest, I =
b) Compound interest, I = P
2. Amount under
a) Simple interest, A =
b) Compound interest, A = P
3. Effective rate of interest when compounding is done k times a year
re =
MIXTURES AND
Important Formulae_for website_for CAT2012 students
RATIO – PROPORTION – VARIATION
1. If a : b : : c : d, then ad = bc
2. If a : b : : c : d, then a + b : b : : c + d : d
3. If a : b : : c : d, then a - b : b : : c - d : d
4. If a : b : : c : d, then a + b : a - b : : c + d : c - d
5. If
then k =
NUMBERS
1. a 3 + b 3 + c3 – 3abc = (a + b + c) (a 2 + b 2 + c2 – ab – bc – ca)
2. The product of n consecutive integers is always divisible by n! (n factorial)
3. The sum of any number of even numbers is always even
4. The sum of even number of odd numbers is always even
5. The sum of odd number of odd numbers is always odd
6. If N is a composite number such that N = a p . b q . cr .... where a, b, c are prime factors of N and p, q, r
.... are positive integers, then
a) the number of factors of N is given by the expression (p + 1) (q + 1) (r + 1) ...
b) it can be expressed as the product of two factors in 1/2 {(p + 1) (q + 1) (r + 1).....} ways
c) if N is a perfect square, it can be expressed
(i) as a product of two DIFFERENT factors in 1/2 {(p + 1) (q + 1) (r + 1) ... -1 } ways
(ii) as a product of two factors in 1/2 {(p + 1) (q + 1) (r + 1) ... +1} ways
d) sum of all factors of N =
e) it can be expressed as a product of two co-primes in 2n–1 ways, where ‘n’ is the number of different prime factors of the given number N
time4education.com/CAT_Important_formulaes/CAT_Important_Formulae.asp
1/11
14/09/2013
Important Formulae_for website_for CAT2012 students
f) the number of co-primes of N (< N), f (N) =
g) sum of the numbers in (e) =
SIMPLE INTEREST AND COMPOUND INTEREST
I = Interest, P is Principle, A = Amount, n = number of years, r is rate of interest
1. Interest under
a) Simple interest, I =
b) Compound interest, I = P
2. Amount under
a) Simple interest, A =
b) Compound interest, A = P
3. Effective rate of interest when compounding is done k times a year
re =
MIXTURES AND