DS time and work problem

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sohailmbaprep: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu Feb 23, 2012 11:18 pm

by sohailmbaprep » Sat Sep 15, 2012 12:00 am

This is from OG 13. COuldn't understand official explanation. pls help

Q) 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.

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Source: Beat The GMAT — Data Sufficiency | Sat Sep 15, 2012 12:00 am

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by GMATGuruNY » Sat Sep 15, 2012 12:22 am

sohailmbaprep wrote:This is from OG 13. COuldn't understand official explanation. pls help

Q) 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.

Statement 1: X produced 30 bottles per minute.
Thus, the work produced by X in 240 minutes = r*t = 30*240.
No information about how much work was produced by Y.
INSUFFICIENT.

Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
Thus, for every bottle Y produced, X produced 2 bottles, implying that X produced 2 of every 3 bottles.
Since X produced 2/3 of the lot in 4 hours, X would need 2 more hours to produce the remaining 1/3 of the lot, for a total of 6 hours.
SUFFICIENT.

The correct answer is B.

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