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collection of tough problems from G PREP - 31

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collection of tough problems from G PREP - 31

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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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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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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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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