Let the work rates of X and Y be x and y respectively

From(1) : (x+y).(2t/3) = x.(t) => x=2y.
We can compare the work rates but we do not know the absolute time required by either of machines.
Insufficient

From(2) : y.(2t) = x.(t) => x=2y. Similar to (1), we need absolute time required to finish the job by at least one f the machines to calculate that of the other.
Insufficient

(1) and (2) gives rise to the same condition. So, even combining (1) and (2), we do not arrive at the answer
Insufficient

Hence, answer E.

Cheers!

Akansha wrote:X and Y work at constant rates, how many more hours does it take machine y,
alone, to fill an order of a certain size than machine X alone.
a. X and Y together fill order in 2�3 the time that X alone does
b. Y alone does it in twice the time as X alone does

OA is E

I selected the correct option but I wanted to get an explanation to understand such type of problems better.

let x works for p hours, and y works for q hours to finish the job;

let the no. of units of job to be done is p*q units;

therefore in 1 hour x will do p*q/p=q units;
and y will do p*q/q=p units;

1) no. of units that x and y will do while working together=p*q/p+q;

now as per the condition we have;
p*q/(p+q)= (2/3)q;
3/2p= p+q;
p=2q;
i.e. y will take twice the time taken by x in completing the job; now since we don't know about the time taken by x in completing the task hence 1 alone is not sufficient to answer the question.

2) p=2q;

which we have proved in last condition, as no new information is provided about the no. of hours taken by x to complete the job hence 2 alone is also not sufficient to answer the question.

combining 1 and 2; no new information is available hence answer should be E

Akansha wrote:X and Y work at constant rates, how many more hours does it take machine y,
alone, to fill an order of a certain size than machine X alone.
a. X and Y together fill order in 2�3 the time that X alone does
b. Y alone does it in twice the time as X alone does

OA is E

I selected the correct option but I wanted to get an explanation to understand such type of problems better.

For people who are less inclined towards deriving formulae, here's something that has worked for me, especially to tackle such DS questions.

The question asks for an absolute value- how many more hours does it take...?

Both the answer stems are talking about a ratio; infact both the answers stems are talking about the same ratio. Hence it takes not more than 20 secs to rightly mark E as an option.