official quant thread for cat08

[amitkrsingh]

Originally Posted by Topgear

Here's one on Time distance...

A starts from P and B starts from Q to meet each other at some time=x.
after crossing each other A takes 16 mins to reach Q and B takes 9 minutes to reach P .. what is x..

I recall some method like x=Square root(t1*t2)

Can neone explain such cases and also other cases with same Questions possible and their solutions..

Let the point where they meet be X.

A takes x mins to travel PX distance and B takes 9 mins to travel PX.
Let speed of A be a and B be b. Then,

a/b = 9/x (If distance is constant then speed is inversely proportional to time)

Similarly B takes x mins to travel QX and A takes 16 mins. Hence,

b/a=16/x

Mutiply both equations to get-

x= 12.

[romy4allcse]

Originally Posted by Topgear

Here's one on Time distance...

A starts from P and B starts from Q to meet each other at some time=x.
after crossing each other A takes 16 mins to reach Q and B takes 9 minutes to reach P .. what is x..

I recall some method like x=Square root(t1*t2)

Can neone explain such cases and also other cases with same Questions possible and their solutions..

x = 12 min.

[poojadatta]

Originally Posted by Topgear

Here's one on Time distance...

A starts from P and B starts from Q to meet each other at some time=x.
after crossing each other A takes 16 mins to reach Q and B takes 9 minutes to reach P .. what is x..

I recall some method like x=Square root(t1*t2)

Can neone explain such cases and also other cases with same Questions possible and their solutions..

The formula you are searching is speed of A/Speed of b =sqrt(time take by b)/sqrt(time taken by a)

[Fuzon]

Originally Posted by Topgear
Here's one on Time distance...

A starts from P and B starts from Q to meet each other at some time=x.
after crossing each other A takes 16 mins to reach Q and B takes 9 minutes to reach P .. what is x..

I recall some method like x=Square root(t1*t2)

Can neone explain such cases and also other cases with same Questions possible and their solutions..

Let a and b be the speeds of A abd B resp, t1 and t2 being the time they travelled before they met.

Now at the time they met, A has travelled at1 (Speed * Time) distance and B has travelled bt2 distance ,

Now after the meet they cross each other and now B has to travel at1 distance in time t and A has to travel bt2 distance in time t

Thus

For A Time needed is t = bt2/a ---1
For B Time needed is t = at1/b ---2

Multuply 1 with 2

t^2=t1*t2
thus
t =Sqrt(t1*t2)

Hope i have managed to explain it properly

[roni_here]

Fermat's little theorem states that:-

if any number p is prime, then (a^p -a)%p = 0 (a is an integer)

so from here we can deduce that a^p % p = a

ex. 2^5 % 5 = 2
3^5 % 5 = 3
2^7 % 7 = 2

so, (a^p/a) % p = 1

and that's the funda we are using here is a^(p-1) % p =1

[Topgear]

Yeah got it !

Thanks..to all.. amit, pooja and Fuzon..

[romy4allcse]

Originally Posted by roni_here

Fermat's little theorem states that:-

if any number p is prime, then (a^p -a)%p = 0 (a is an integer)

so from here we can deduce that a^p % p = a

ex. 2^5 % 5 = 2
3^5 % 5 = 3
2^7 % 7 = 2

so, (a^p/a) % p = 1

and that's the funda we are using here is a^(p-1) % p =1

ya understood now...thanx a lot

[deep@k]

Originally Posted by poojadatta

thanks but what I wrote was it wrong.... and if so where....

answer is correct but you are writing 2x that is wrong instead of that 8x has to come...............

[poojadatta]

deep@k thanks so it is it like when it a^-b we calculate the power and put that value I mean when it is 2^-3 we take 8x when 3^-2 we will take 9....right?

[deep@k]

Originally Posted by poojadatta

deep@k thanks so it is it like when it a^-b we calculate the power and put that value I mean when it is 2^-3 we take 8x when 3^-2 we will take 9....right?

ya exactly because here a^-b will go to denominator so the divisibility rule will applied for that also ....

It is not like that like for 2^-3 you have to take 8x and for 3^-2 you have to consider 9x it completely depends on the numerator .... please see more example on number system....

or other wise you can visit the number system thread for more example......