gmacforjyoab wrote:
A newer machine, working alone at its constant rate, can fill a production order in half the time required by two older machines working together at their constant rates. If the three machines are used together, will they require more than 1 hour to fill a production order?
(1) Each of the older machines, working alone at its constant rate, can fill half a production order in less than 4 hours.
(2) If the newer machine were to double its rate, it could fill a production order working alone in less than one hour
Hi jyothi,
I think picking up few nos for each statements is perhaps the fastest way to do this.Before doing this assume x+y is time taken by older machines and z by new machine
1)for 1st statement the older machines can fill the order in less than 4 hours , take for instance the time taken by 2 older machines be 6 hours,
so half-the production order will be in x+y/2=3 hours
time taken by new machine is 3 hours,
so in 6 hours 1.5 production order is filled
=> 1 production order in= 6/1.5= 4 hours (so answer to the statement is no)
but let us assume time taken by older machines x+y=1/4 hours
so half the prod order = 1/4*1/2=1/8
and z takes (1/4*1/2)=1/8
so in 1/4 hours 1.5 orders
1 prod order in 1/4*1/1.5 (which will be less than 1 hour, so answer is yes)
clearly therefore statment 1 is insufficient
so
2)for the answer to be yes (i,e statement sufficient to state it will take less than 1hour you can pick the same values as in 2 conditio of 1st statement i,e x+y=1/2 hours)
for the yes condition pick time taken by z = 10/6 ,, so if rate doubled it will be able to do in 5/6 hours,,
so x+y= 20/6
so in 30/6 2 orders are completed,
=> 1 order in 5/2 hours (so answer is no as order cannot be completed in less than in 1 hour),,
you can have the same value (z=10/6) and use it for statemet 1 as well.
hence both the values are insufficient.E is correct