official quant thread for cat08

[guneet_01]

Shaurya and Ajit take a straight route to the same terminal point and travel with constant speeds. At the initial moment, the positions of the two and the terminal point form an equilateral triangle. When Ajit covers a distance of 80 km, the triangle becomes right-angled. When Arjit was at a distance of 120 km from the terminal point, Shaurya arrived at the point. Find the distance between them at the initial moment assuming that there are integral distances throughout the movements described.
(a) 300 km
(b) 240 km
(c) 200 km
(d) 225 km
(e) 275 km

[apatchofsnow]

Originally Posted by guneet_01

Shaurya and Ajit take a straight route to the same terminal point and travel with constant speeds. At the initial moment, the positions of the two and the terminal point form an equilateral triangle. When Ajit covers a distance of 80 km, the triangle becomes right-angled. When Arjit was at a distance of 120 km from the terminal point, Shaurya arrived at the point. Find the distance between them at the initial moment assuming that there are integral distances throughout the movements described.
(a) 300 km
(b) 240 km
(c) 200 km
(d) 225 km
(e) 275 km

Working from the options ,
I get the answer as option B 240 km...

[getintoiimb]

puys pls help me with these qns

1)if a,b,c are in GP then log a,log b,log c are in
a)AP b)GP c)HP d)none

2)the sum of an infinite GP whose common ratio is < 1is 32 and the sum of the first two terms is 24.what will be the 3rd term?
a)2 b)16 c)8 d)12 e)4

3)what will be the value of x^1/2.x^1/4.x^1/8 to infinity
a)x^2 b)x c)x^3/2 d)x^3

pls let me know ur approach as well

[Iota]

Originally Posted by guneet_01

Shaurya and Ajit take a straight route to the same terminal point and travel with constant speeds. At the initial moment, the positions of the two and the terminal point form an equilateral triangle. When Ajit covers a distance of 80 km, the triangle becomes right-angled. When Arjit was at a distance of 120 km from the terminal point, Shaurya arrived at the point. Find the distance between them at the initial moment assuming that there are integral distances throughout the movements described.
(a) 300 km
(b) 240 km
(c) 200 km
(d) 225 km
(e) 275 km

let the total distance be = D km; and the speed be A kph and S kph.
S/A = D/(D-120).
when Arijit goes 80 km Shaurya goes 80D/(D-120) km

so we have the right angled triangle with the angles 60,30 & 90.
(D-80D/(D-120))= (D-80)Sin30
solving we get, D = 240 km

[rahul_4096]

Originally Posted by gaggi_85

these questions will give u 8 marks in cat and i think just by solving as solved by Rahul u can get it..
dont expect shortcuts everytime...

absolutely correct

and BTW as far as I remember, this was the only double question in cat 2007 which cannot be solved only by matching options. Rest all double question sets can be tackled by putting options of 2nd question in condition given in first one.

and last but not least, I expect out of all ppl active on this thread and on future qqad 2008 threads, at least 90% will be engineers. Hence I do not mind using lighter variety of calculus.

[jha16june]

Originally Posted by getintoiimb

puys pls help me with these qns

1)if a,b,c are in GP then log a,log b,log c are in
a)AP b)GP c)HP d)none

2)the sum of an infinite GP whose common ratio is < 1is 32 and the sum of the first two terms is 24.what will be the 3rd term?
a)2 b)16 c)8 d)12 e)4

3)what will be the value of x^1/2.x^1/4.x^1/8 to infinity
a)x^2 b)x c)x^3/2 d)x^3

pls let me know ur approach as well

1. a.)AP b/a=c/b => log(b/a)=log(c/b) => logb-loga=logc-loga
2. e)4 a/(1-r)=32 and a(1+r)=24
3. b)x GP series.

[Iota]

Originally Posted by getintoiimb

puys pls help me with these qns

1)if a,b,c are in GP then log a,log b,log c are in
a)AP b)GP c)HP d)none

b^2 = ac
2logb = loga + logc
hence in A.P

[naga25french]

Originally Posted by getintoiimb

puys pls help me with these qns

1)if a,b,c are in GP then log a,log b,log c are in
a)AP b)GP c)HP d)none

2)the sum of an infinite GP whose common ratio is < 1is 32 and the sum of the first two terms is 24.what will be the 3rd term?
a)2 b)16 c)8 d)12 e)4

3)what will be the value of x^1/2.x^1/4.x^1/8 to infinity
a)x^2 b)x c)x^3/2 d)x^3

pls let me know ur approach as well

answers

1. a.)AP
2. e)4
3. b)x

confirm it i will post the soln..

[naga25french]

if the numbers are in gp means then b^2 = ac..

taking log on both sides

log b^2 = log ac

2logb = log a + log c

there fore log a , log b , log c are in ap...

[rahul_4096]

Originally Posted by getintoiimb

puys pls help me with these qns


3)what will be the value of x^1/2.x^1/4.x^1/8 to infinity
a)x^2 b)x c)x^3/2 d)x^3

pls let me know ur approach as well

x^1/2.x^1/4.x^1/8...

x^(1/2 + 1/4 + 1/8 .......)

x^({1/2}/{1-1/2})

x^1

(b)

Originally Posted by getintoiimb

2)the sum of an infinite GP whose common ratio is < 1is 32 and the sum of the first two terms is 24.what will be the 3rd term?
a)2 b)16 c)8 d)12 e)4

let first term be 'a' & common ratio be 'r'

32 = a / (1-r).........(1)

a + ar = 24.............(2)

by (1) & (2)

r^2 = 1/4
a = 16

third term = ar^2 = 16/4 = 4

(e)