collection of tough problems from G PREP - 31 - The Beat The GMAT Forum

collection of tough problems from G PREP - 31

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Mon Feb 08, 2010 3:22 am

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 | Mon Feb 08, 2010 3:22 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 4:11 am

abhasjha wrote: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.

st 1: 30 bottles per min. --- not sufficient we don't how much part it has done waht is the entire lot.
st2: let total work be W so X produce 2/3 W in 4 hrs
Y produce 1/3 w IN 3 HRS.
SO IN 1 HR, X produce (2/3)/4 W= 1/6 W so it will take 6 hrs. Ans.

ans is B

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Feb 08, 2010 4:33 am

abhasjha wrote: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) helps us compute machine X's work in 4 hours, and not that of machine Y's at the same time, and in the absence of the total work to be done, we won't be able to determine how long it would take machine X do it. Insufficient

(2) If machine X can do 2/3 of the total job in 4 hours, then how long will it take to complete the entire job by itself, can be determined. Sufficient

[spoiler]B[/spoiler]

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Tue Feb 09, 2010 1:17 am

abhasjha wrote: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.

Say X produces x bottles per hour and Y produces y bottles per hour
Total production lot = 4x +3y

Machine x would take = (4x+3y)/x = 4+3*(y/x) hours

1) x = 30 not sufficient -we need to know y/x or x and y both
2) 4x = 2(3y) = >y/x = 2/3

Machine x would take 4+3*2/3 = 6 hours - Sufficient

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