collection of tough problems from G PREP - 12

[abhasjha]

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?

1) x = 48

2) y = 20

[harsh.champ]

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?

1) x = 48

2) y = 20

IMO C.

Quite evident in the question.

Are there any traps??
I suspect it,but also hope there aren't any...

[ajith]

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?

1) x = 48

2) y = 20

Time took to travel first y kms = y/x
Time took to travel next 40-y = (40-y)/1.25x

Total time took = y/x+40/1.25x -y/1.25x
= y/x(1-1/1.25) +40/1.25 *1/x
= 0.2 y/x + 32/x

Time taken if she traveled at speed x = 40/x

ratio = 0.2y+32/40

1.) insufficient
2) sufficient

B for me

[abhasjha]

OA is B

[papgust]

Total time took = y/x+40/1.25x -y/1.25x
= y/x(1-1/1.25) +40/1.25 *1/x
= 0.2 y/x + 32/x

Time taken if she traveled at speed x = 40/x

ratio = 0.2y+32/40

1.) insufficient
2) sufficient

B for me

Ajith,

Why have you subtracted by y/1.25x? I guess i'm missing the logic behind it.

[harsh.champ]

Total time took = y/x+40/1.25x -y/1.25x
= y/x(1-1/1.25) +40/1.25 *1/x
= 0.2 y/x + 32/x

Time taken if she traveled at speed x = 40/x

ratio = 0.2y+32/40

1.) insufficient
2) sufficient

B for me

Ajith,

Why have you subtracted by y/1.25x? I guess i'm missing the logic behind it.

Ok,I get it.
The answer will be B.

Hey papgust,
Note that ajith has just added the 2 equations to get the 3rd equation.

Time took to travel first y kms = y/x
Time took to travel next 40-y = (40-y)/1.25x

He has not subtracted y/1.25x separately.It looks like that just because he has separated the tems 40/1.25x and -y/1.25x
(40-y) because total distance = 40 miles and y miles at avg. speed of x.

I guess it is clear now.