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13 Jun 2024, 01:30
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D
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Difficulty:
35%
(medium)
Question Stats:
78% (01:56) correct
22%
(02:14)
wrong
based on 90
sessions
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Machines Y and Z work at their respective constant rates. If it takes machines Y and Z, working together, 12 hours to fill a production order of a certain size, how many more hours does it take machine Y, working alone, to fill the order than it takes machine Z, working alone?
(1) Machine Z, working alone, fills a production order of this size in twice the time than machine Y, working alone, does
(2) Machines Y and Z, working together, fill a production order of this size in two-thirds the time that machine Y, working alone, does
(1) Machine Z, working alone, fills a production order of this size in twice the time than machine Y, working alone, does
(2) Machines Y and Z, working together, fill a production order of this size in two-thirds the time that machine Y, working alone, does
13 Jun 2024, 02:14
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Bunuel
Machines Y and Z work at their respective constant rates. If it takes machines Y and Z, working together, 12 hours to fill a production order of a certain size, how many more hours does it take machine Y, working alone, to fill the order than it takes machine Z, working alone?
(1) Machine Z, working alone, fills a production order of this size in twice the time than machine Y, working alone, does
(2) Machines Y and Z, working together, fill a production order of this size in two-thirds the time that machine Y, working alone, does
(1) Machine Z, working alone, fills a production order of this size in twice the time than machine Y, working alone, does
(2) Machines Y and Z, working together, fill a production order of this size in two-thirds the time that machine Y, working alone, does
Given:
Y + Z = 12hours
To find : Y-Z (working alone)
AD/BCE
St.1: If Y takes x hours, accordingly Z takes 2x hours. No particular information about Y or Z given so not alone sufficient
What remains to us is BCE
St.2: Y + Z takes 2/3rd time of Y alone.
A bit confusing but I cracked it this way
12 x 1.5 we get 18. Checking it backwards as per the statement 2. Y takes 18 so 2/3 of 18 is 12. So we are correct.
We get Y as 18 but have no idea about Z therefore even B is not sufficient.
Taking both together we get Z as 36
Therefore C is the Answer
Posted from my mobile device
13 Jun 2024, 03:22
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IMO D,
Given - Machines Y and Z work at their respective constant rates (assuming those as y and z per hour respecitively). If it takes machines Y and Z, working together, 12 hours to fill a production order of a certain size (assuming w).
Therefore, w = 12(y+z) ----- (Eq1)
To calculate, how many more hours does it take machine Y, working alone, to fill the order than it takes machine Z, working alone lets check the given statements,
1st - Machine Z, working alone, fills a production order of this size in twice the time than machine Y, working alone, does (assuming y worked for t hours)
w = z*2t = y*t
Therefore, y=2z
substituting this in equation 1 we will get,
12(y+z) = z*2t,
as y=2z,
12*3z = z*2t
t=18 hours,
t' time for machine Z to complete the same order = 2*t = 36Hours,
So, machine Y doesnt take more time than Z. Hence Sufficient.
2nd - Machines Y and Z, working together, fill a production order of this size in two-thirds the time that machine Y, working alone, does (again assuming same y worked for t hours)
from this the equation we can get,
(2t/3) * (y+z) = y*t
on further solving,
2(y+z) = 3y
y=2z.
This is same we got from statement 1. Hence Sufficient.
But, machine Y doesnt take more time than Z. and question ask us to calculate "how many more hours does it take machine Y, working alone, to fill the order than it takes machine Z, working alone?"
Is there anything i am missing? Experts please advice?
Given - Machines Y and Z work at their respective constant rates (assuming those as y and z per hour respecitively). If it takes machines Y and Z, working together, 12 hours to fill a production order of a certain size (assuming w).
Therefore, w = 12(y+z) ----- (Eq1)
To calculate, how many more hours does it take machine Y, working alone, to fill the order than it takes machine Z, working alone lets check the given statements,
1st - Machine Z, working alone, fills a production order of this size in twice the time than machine Y, working alone, does (assuming y worked for t hours)
w = z*2t = y*t
Therefore, y=2z
substituting this in equation 1 we will get,
12(y+z) = z*2t,
as y=2z,
12*3z = z*2t
t=18 hours,
t' time for machine Z to complete the same order = 2*t = 36Hours,
So, machine Y doesnt take more time than Z. Hence Sufficient.
2nd - Machines Y and Z, working together, fill a production order of this size in two-thirds the time that machine Y, working alone, does (again assuming same y worked for t hours)
from this the equation we can get,
(2t/3) * (y+z) = y*t
on further solving,
2(y+z) = 3y
y=2z.
This is same we got from statement 1. Hence Sufficient.
But, machine Y doesnt take more time than Z. and question ask us to calculate "how many more hours does it take machine Y, working alone, to fill the order than it takes machine Z, working alone?"
Is there anything i am missing? Experts please advice?
