official quant thread for cat08

[IIM maniac]

Paul was swimming against the stream in a river with his cap on, at point A, his cap fell off into the river. Intent on getting his strokes right, Paul did not notice this. He realized he had lost his cap only after 15 min. He turned back and chased his cap that was floating away from him. He caught his cap at point B exactly 2 KMS from point A. Can you determine the speed of the stream?
a) 6 b) 3 c) 4 d) 5
I think all must be knowing this question but i am not posting this just for the sake getting it solved, but for the approach of solving it.
Regards

[parmindersaluja]

for the first one i think its (11/3)^(3/2)

and second one is 30. If u confirm the answers, i may give the explanations or correct me and give the soluti.

well solve this on
Three circles A, B and C have a common centre O.
A is the inner circle, B middle circle and C is outer circle. The
radius of the outer circle C, OP cuts the inner circle at X and
middle circle at Y such that OX = XY = YP. The ratio of the
area of the region between the inner and middle circles to
the area of the region between the middle and outer circle
is:
(A)1/3
(B)2/5
(C)3/5
(D)1/5

[IIM maniac]

Originally Posted by parmindersaluja

for the first one i think its (11/3)^(3/2)

and second one is 30. If u confirm the answers, i may give the explanations or correct me and give the soluti.

well solve this on
Three circles A, B and C have a common centre O.
A is the inner circle, B middle circle and C is outer circle. The
radius of the outer circle C, OP cuts the inner circle at X and
middle circle at Y such that OX = XY = YP. The ratio of the
area of the region between the inner and middle circles to
the area of the region between the middle and outer circle
is:
(A)1/3
(B)2/5
(C)3/5
(D)1/5

Answer would be 3/5

[stalwart_itsme]

Originally Posted by parmindersaluja

for the first one i think its (11/3)^(3/2)

and second one is 30. If u confirm the answers, i may give the explanations or correct me and give the soluti.

its correct.... share your approach...!!!!

[parmindersaluja]

Originally Posted by stalwart_itsme

Yup.... its correct.....
Enjoy solving this too...

#)If the sum of the product of three positive real numbers taking two at a time is 11, then
what is the maximum possible value of the product of these three numbers?
1. 11/3
2 6^(3/2).
3 (11/3)^(3/2)
4 (11/2)^(4/3)
5. None of these

#)In how many ways 3 identical books may be distributed among 5 students such that no student
gets more than 2 books?
1. 125 2. 64 3. 48 4. 40 5. 30

Puys post some more questions...

ab+bc+ca=11
for max product ab=bc=ca=11/3
=>a=b=c=sq rt 11/3

second one
books can be distributed as 1 each to 3 out of 5 =>5C3=10
or 2 to one out of 5 and 1 to one =>5C1*4C1=20
total 30

[parmindersaluja]

Originally Posted by IIM maniac

Paul was swimming against the stream in a river with his cap on, at point A, his cap fell off into the river. Intent on getting his strokes right, Paul did not notice this. He realized he had lost his cap only after 15 min. He turned back and chased his cap that was floating away from him. He caught his cap at point B exactly 2 KMS from point A. Can you determine the speed of the stream?
a) 6 b) 3 c) 4 d) 5
I think all must be knowing this question but i am not posting this just for the sake getting it solved, but for the approach of solving it.
Regards

i solved the equation
(2/s) = 1/4 + ((p-s)/4(p+s)) + 2/(p+s)

=>s=4
where p=paul's speed, s= stream speed.

but can anybody give a better approach than this

[dashing]

Originally Posted by parmindersaluja

for the first one i think its (11/3)^(3/2)

and second one is 30. If u confirm the answers, i may give the explanations or correct me and give the soluti.

well solve this on
Three circles A, B and C have a common centre O.
A is the inner circle, B middle circle and C is outer circle. The
radius of the outer circle C, OP cuts the inner circle at X and
middle circle at Y such that OX = XY = YP. The ratio of the
area of the region between the inner and middle circles to
the area of the region between the middle and outer circle
is:
(A)1/3
(B)2/5
(C)3/5
(D)1/5

answer 3/5

let OX be r
radius of bigger circle 3x
middle one 2x
small one x

so diff between small and middle areas = k3
diiff between bigger and middle = k5

so ratio 3/5

[IIM maniac]

Originally Posted by parmindersaluja

i solved the equation
(2/s) = 1/4 + ((p-s)/4(p+s)) + 2/(p+s)

=>s=4
where p=paul's speed, s= stream speed.

but can anybody give a better approach than this

I have solved it using different way
We will consider the concept of relative speed,
speed of paul in still water = p
speed of cap = s(as its going with stream)
stream speed = s
speed of paul against stream = p-s
since cap ans paul are moving in opposite direction, relative speed of paul
wrt cap is p-s+s = p
Now going for catching the cap, paul is going with stream, so his speed
wrt cap is p+s-s = p
This means paul has constant relative speed throught, so time needed to
reach C is same as time needed to reach C from B, which is 15 min + 15
min = 30 min or 1/2 hr
now speed = 2KM/1/2 = 4

[dashing]

Originally Posted by stalwart_itsme

its option b. (2√2 -1)/2

hi stalwart

could you please tell the approach

[stalwart_itsme]

Originally Posted by dashing

hi stalwart

could you please tell the approach

join OD
its given that diameter is 3
so OD is 1.5
since MN is divided in the ratio 1:2
so NL is 1 and ML is 2
ON=1.5
so OL=ON-NL which is 0.5 or 1/2
DF is perpendicular to MN
So EH is also 0.5
applying pythogoras theorem triangle ODL we get DL=2^(1/2)
similarly E divides AB in ratio 1:2.. so OE is 0.5 or (1/2) so HL is 1/2
so DH = DL-HL =(√2-1/2)= (2√2 -1)/2

Correct me if i m wrong..!!!!