official quant thread for cat08

[implex]

Originally Posted by Hi2All

Hi friends...
There are 40 seats in a bus. People agree to share the money for the number of seats. The total money comes to 70.37. How many seats were free?

The trick here is to find a prime number less than 40 which divides 70.37!!
that will suffice

[implex]

Originally Posted by linksuresh

also, could someone also explain how to calculate the minimum value for the question 87

minimum can be zero!!

[implex]

official solution 90)

It is easy to figure out speed of ali is 60 kmph and that of Bobby is 40 ( given) and also the distnace between them can be found out to be 50 kmph
they meet for the first time in 50/100=30 mins
thereafter they need to travel 100 km ( both together) relative speed is 100 so time is 1 hour

the trick here is to see that even if they travel in the same direction for a part of the journey that gets made up by the part they travel in opposite direction!

There is a goof up in the options. I am sorry for that X(4) should be 3:30

This can be seen by this . at 2:30 both ali and bobby will be at town B.
in 50 minutes ali will reach town A and bobby will be close to it
in the next ten minutes ali will come back 10 km and bobby will have reached 40 kms from B now 40+10=50
so they meet at 3:30

[bhavin422]

Originally Posted by implex

minimum can be zero!!

hey implex...1 doubt....min value of xy+yz+zx can be zero when x,y,z <= 0
but in d given sum...x,y,z <0 ...what is the min value then??

[bhavin422]

Originally Posted by implex

official solution 90)

It is easy to figure out speed of ali is 60 kmph and that of Bobby is 40 ( given) and also the distnace between them can be found out to be 50 kmph
they meet for the first time in 50/100=30 mins
thereafter they need to travel 100 km ( both together) relative speed is 100 so time is 1 hour

the trick here is to see that even if they travel in the same direction for a part of the journey that gets made up by the part they travel in opposite direction!

There is a goof up in the options. I am sorry for that X(4) should be 3:30

This can be seen by this . at 2:30 both ali and bobby will be at town B.
in 50 minutes ali will reach town A and bobby will be close to it
in the next ten minutes ali will come back 10 km and bobby will have reached 40 kms from B now 40+10=50
so they meet at 3:30

ok..thought so...that x(4) should be 3:30...so all of these is the answer

[implex]

Originally Posted by bhavin422

hey implex...1 doubt....min value of xy+yz+zx can be zero when x,y,z <= 0
but in d given sum...x,y,z <0 ...what is the min value then??

the thing is if we assume that two of (x,y,z) are very small say h, where h tends to zero
then also xy+yz+zx will be just greater than zero and we will not be wrong if we assume that value to be zero in the limiting case.

[amitkrsingh]

official solution 90)

It is easy to figure out speed of ali is 60 kmph and that of Bobby is 40 ( given) and also the distnace between them can be found out to be 50 kmph
they meet for the first time in 50/100=30 mins
thereafter they need to travel 100 km ( both together) relative speed is 100 so time is 1 hour

the trick here is to see that even if they travel in the same direction for a part of the journey that gets made up by the part they travel in opposite direction!

There is a goof up in the options. I am sorry for that X(4) should be 3:30

This can be seen by this . at 2:30 both ali and bobby will be at town B.
in 50 minutes ali will reach town A and bobby will be close to it
in the next ten minutes ali will come back 10 km and bobby will have reached 40 kms from B now 40+10=50
so they meet at 3:30

Yeah that will make all of them as true. So, my method was correct. I thought a lot after u said that answer is not correct but couldn't come up with better approach. Thanks by the way for nicce questions. . Keep it up

[linksuresh]

Originally Posted by implex

The trick here is to find a prime number less than 40 which divides 70.37!!
that will suffice

as per ur logic, that wud be 31 commuters.. givin 2.27 per head...

could u elaborate more on why it shd be prime.. as in wats the logic ?

[implex]

Originally Posted by linksuresh

as per ur logic, that wud be 31 commuters.. givin 2.27 per head...

could u elaborate more on why it shd be prime.. as in wats the logic ?

as there is equal amount contributed by all, so 70.37 should be divisible by a prime. if it is not prime then we will get many values and then we won't be able to decide how many people are seated and how many are vacant.

[Hi2All]

Originally Posted by implex

as there is equal amount contributed by all, so 70.37 should be divisible by a prime. if it is not prime then we will get many values and then we won't be able to decide how many people are seated and how many are vacant.

sorry friend.. i am unable to understand..
u told it should be a prime...why can't it be anyother prime number(i.e 37,29..) other than 31..
please giv me some more explanation..so that i can understand..

Thanxx..