Data Sufficiency

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?
(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours.

(1) Machine X produced 30 bottles per minute.

We dont know the no of bottles in the production lot.

Insufficient

(2) Machine X produced twice as many bottles in 4 hours as machine Y produced in 3 hours.

Lets say Machine X produced x in 4 hrs, and M/c Y produced y in 3 hrs

x = 2y
y = x/2

Total no of bottles = x+x/2 = 3x/2

x bottles ========== 4hrs
3x/2 bottles ======= 6 hrs

Sufficient

Option A

let X takes x hours and Y takes y hours.
X works 4 hours => X's fraction of work = 4/x
Y works 3 hours => Y's fraction of work = 3/y
from given = both fractions should add to 1 => 4/x+3/Y = 1 => 4y+3x = xy
we need to find x in above equation.
1) this is insufficient as we dont know the definition of producing how many bottles equals 1 job.
hence insufficient.
2) here,
X - 2p bottles - 4 hours
Y - p bottles - 3 hours
X - p bottles - 2 hours
so y = 1.5x hoours
so substituting we get x = 6 hrs. hence sufficient.

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