official quant thread for cat08

[Varun Khullar]

Originally Posted by Niki_10

3 boys can be paired with 3 girls in
7C3*3! ways

and 4 girls can be paired in 3 ways

so total ways is 7c3*3!*3=630.

Let me know if it is rite..

both are correct.

[amitkrsingh]

Originally Posted by amitkrsingh

Q) Show that the equation
x^2 - 3y^2 = 17
has no solutions in integers.

This question was from Suresh's blog -

3y^2= x^2-17

Let x = 3k+t where t=0,1 or 2

Hence,
3y^2 = 9k^2 +6kt + t^2 -17
=(9K^2+6kt-18 ) + (t^2+1)

Since RHS should be a multiple of 3.Hence, t^2+1 should be a multiple of 3
t^2+1 = 1,2,5 for t=0,1,2

Hence, no integer soln is possible

[Varun Khullar]

Originally Posted by amitkrsingh

This question was from Suresh's blog -

3y^2= x^2-17

Let x = 3k+t where t=0,1 or 2

Hence,
3y^2 = 9k^2 +6kt + t^2 -17

basically its diophantine
aryabhatta bramhaputra solved these..
then the europeans who renamed them as Diophantine

x^2 = 4k+1 or 4k
y^2 = 4p+1 or 4p
x^2 -3y =17
we can used this disprove all cases ..using odd even nature of 4k and 4k+1..

[romy4allcse]

Q) Show that the equation
x^2 - 3y^2 = 17
has no solutions in integers.

Can't we do it in this way

x^2 - 3y^2 = 17
(x + y*sqrt(3))(x - y*sqrt(3)) = 17

RHS is a prime no so has no factor except 1 and 17
let (x + y*sqrt(3)) = 1 && (x - y*sqrt(3)) = 17
solving these two eq.
2x = 18
x = 9 & y = -8/sqrt(3) which is not an integer

similarly if (x + y*sqrt(3)) = 17 && (x - y*sqrt(3)) = 1solving these two eq.
x = 9 & y = 8/sqrt(3)

Hence it is proved that this eq. has no integral solution(x,y)

waiting for the feedback.....

[vineet.nitd]

Originally Posted by romy4allcse

Q) Show that the equation
x^2 - 3y^2 = 17
has no solutions in integers.

Can't we do it in this way

x^2 - 3y^2 = 17
(x + y*sqrt(3))(x - y*sqrt(3)) = 17

RHS is a prime no so has no factor except 1 and 17
let (x + y*sqrt(3)) = 1 && (x - y*sqrt(3)) = 17
solving these two eq.
2x = 18
x = 9 & y = -8/sqrt(3) which is not an integer

similarly if (x + y*sqrt(3)) = 17 && (x - y*sqrt(3)) = 1solving these two eq.
x = 9 & y = 8/sqrt(3)

Hence it is proved that this eq. has no integral solution(x,y)

waiting for the feedback.....

You are assuming tht 17 is a product of 2 integers.

[ankaj]

here is the concept of euler...credit Shivam bhai....

[naiquevin]

I found an attachment on this thread named quantproblemset1.pdf (1-100)
..does anybody have the answer key to this set?

[gaggi_85]

Aaj itni chuppi kyun hai yahan

One from my side...

There are five consecutive integers a, b, c, d and e such that a < b < c < d < e and
a^2 + b^2 + c^2 = d^2 + e^2 . How many possible values of b can be there?


1) 3
2) 1
3) 2
4) 4
5) 0

[gaggi_85]

Another one....

What is the probability that product of two integers chosen at random has the same unit’s digit as
the integers themselves?

[MaskedMenace]

Originally Posted by gaggi_85

Aaj itni chuppi kyun hai yahan

One from my side...

There are five consecutive integers a, b, c, d and e such that a < b < c < d < e and
a^2 + b^2 + c^2 = d^2 + e^2 . How many possible values of b can be there?


1) 3
2) 1
3) 2
4) 4
5) 0

only 1 i think ...

10,11,12,13,14