collection of tough problems from G PREP - 21

[abhasjha]

Machine X and Y work at their respective constant rates. How many more hours does it take Machine Y, working alone, to fill a production order of a certain size than it takes Machine X, working alone?

1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.

2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

[harsh.champ]

Machine X and Y work at their respective constant rates. How many more hours does it take Machine Y, working alone, to fill a production order of a certain size than it takes Machine X, working alone?

1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.

2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

Let working rate of machine X = x units/hr and
working rate of machine Y = y units/hr

Statement 1:- x+y = (3/2)x
Statement 2:- x=2y ,it is similar to statement 1

Taking both the statements together,[spoiler]also since we don't have the no. of hours ,we are unable to determine the answer.[/spoiler]
IMO E is the answer.

[ajith]

Machine X and Y work at their respective constant rates. How many more hours does it take Machine Y, working alone, to fill a production order of a certain size than it takes Machine X, working alone?

1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.

2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

Let the speed of the machine X x and speed of machine Y y
1. T/x+y = 2/3 (T/x) = >1/(x+y) = 2/(3x)
2. T/y= 2(T/x) => 2y =x

1. Insufficient
2. Insufficient

Combined 1&2 contradicts

[spoiler]IMO E (Please do not post only this part, honestly it doesn't help other than to increase your post count)[/spoiler]

[abhasjha]

OA - E

[sanju09]

Machine X and Y work at their respective constant rates. How many more hours does it take Machine Y, working alone, to fill a production order of a certain size than it takes Machine X, working alone?

1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.

2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

If Machine X and Y working at their respective constant rates fill a production order of given size in x hours and y hours, respectively, then the tone of the question suggests that y > x, and question is y - x =?

(1) Tells (x y)/(x + y) = (2 x)/3, which simplifies to y = 2 x, and y - x = x or ½ y, we don't know either. Insufficient

(2) Is a replicate of (1), y = 2 x. Insufficient

There's no point in coalescing identical info.

[spoiler]E[/spoiler]

also see

https://www.beatthegmat.com/ds-machines- ... 43602.html