official quant thread for cat08

[masoom]

if 'a' is an odd number and 'b' is an even number then what is the otal number of solutions of :

ab+2= 2a+b+600

[ahaprashant]

I guess we still have to answer this one:
A country has 1998 airports connected by some direct flights.For any three airports, some two are not connected by a direct flight.What is the maximum number of direct flights that can be offered?
My answer was: 1332

[MaskedMenace]

Originally Posted by masoom

if 'a' is an odd number and 'b' is an even number then what is the otal number of solutions of :

ab+2= 2a+b+600

2 solutions ??

i assumed a = 2m+1, b = 2m

[masoom]

Originally Posted by MaskedMenace

2 solutions ??

i assumed a = 2m+1, b = 2m

nopes try again....

and how did u proceed after assuming..

[naiquevin]

Originally Posted by masoom

if 'a' is an odd number and 'b' is an even number then what is the otal number of solutions of :

ab+2= 2a+b+600

is the answer 12?

(b-2) (a-1) = 600

6 pairs of even factors of 600, each giving 2 values of a and b

[naga25french]

Originally Posted by masoom

if 'a' is an odd number and 'b' is an even number then what is the otal number of solutions of :

ab+2= 2a+b+600

ab+2= 2a+b+600

2a+b-ab-2 = 600

2(a-1) - b(a -1) = 600

(a-1)(2-b) = 600

since a is odd and b is even

so (a-1) and (2-b) is even

600 = 2^3 * 5^2 * 3

no of factors are 24

of these 1,3,5,15,25,75 can be ruled out

so the possible solution is 6 ...

since its not ordered pairs we can write 6 * 2 = 12

so totally 12 solutions

[masoom]

Originally Posted by naga25french

ab+2= 2a+b+600

2a+b-ab-2 = 600

2(a-1) - b(a -1) = 600

(a-1)(2-b) = 600

since a is odd and b is even

so (a-1) and (2-b) is even

600 = 2^3 * 5^2 * 3

no of factors are 24

of these 1,3,5,15,25,75 can be ruled out

so the possible solution is 6 ...

since its not ordered pairs we can write 6 * 2 = 12

so totally 12 solutions

yups naga/naieqevin ryt ans..

[ahaprashant]

Originally Posted by MaskedMenace

2 solutions ??

i assumed a = 2m+1, b = 2m

Hey
a = 2m+1, b = 2n, should be more appropriate assumption, right ?
By assuming so (only m), you're necessarily putting some constraints!

[MaskedMenace]

Originally Posted by masoom

nopes try again....

and how did u proceed after assuming..

m^2 - m - 150 = 0

m*(m-1) = 150

i see no 'm' is possible here..how to go ?

[masoom]

Originally Posted by MaskedMenace

m^2 - m - 150 = 0

m*(m-1) = 150

i see no 'm' is possible here..how to go ?

@masked...

the fallacy here is that u considered 2 consecutive numbers...

if odd= 2m+1 and even = 2m...

then they are consecutive numbers...

which is not the constrant in question....

and the matter of fact no consecutive numbers are sartisfying,,