gmatacequants wrote:
russ9 wrote:
Hi MacFauz,
I see how you come up with the two equation but how that leads to the solution is still rather unclear. The question ask's How many tablets does Machine A produce in the time that it takes Machine B to catch up?
Don't you need to know the individual rates to come to the conclusion? These statements are giving us the relative rates, which is fine but how can you tell how long it'll take machine B to make 30 additional tablets without knowing the difference between the two and the rate of A?
Hi Russ9 ,
This one is tricky and more you practice,the more hang you should get for such q's.
Nevertheless,to make this concept clear :
Suppose the production rate for
m/c A is "
a" tablets per unit time
and m/c B is "
b" tablets per unit time
Now, as per problem statement,if for time t,B produces (during which A is also producing);then
b*t-a*t = 30
=> a*t (b/a-1) = 30
=> a*t = 30 / (b/a-1) ------ (1)
where no. of tablets m/c A produces in the time when m/c B catches up
that is during t = a*t
Now, finding this value boils down to finding the ratio b:a
for which each option could be checked:
option 1:
a = 2*(b-a) ------ as B is faster so as to catch up
=> 3*a = 2*b
=> b/a = 3/2 which gives a*t =60 using (1)
option 2:
a+b = 5*(b-a)
=> 6*a = 4*b
=> b/a = 3/2 which again gives a*t =60 using (1) So, either option is independently sufficient.Best form of appreciation is KudosAnother way of solving it could be by assuming a and b to be the units of time it takes A and B to make 1 tablet, respectively. Then, if t is the total time starting after machine B joins and ending when machine B has made as many tablets as A, t/a and t/b are the number of tablets machine A and machine B have made in time t, respectively.
Hence, according to info in the quest, we have:
30 + t/a = t/b . Let this be equation (1)
1) This gives us
(1/a)=2(1/b - 1/a) [Machine b's rate is higher according to info in the question]
=> 3b=2a
Substituting this in equation (1), we get t=90b
Hence, t/b = 90 and t/a=60. This means a makes 60 tablets AFTER b has joined. Together they make 90 tablets each. INFORMATION 1 IS SUFFICIENT.
2) This gives us
1/a + 1/b = 5(1/b - 1/a) => 6b=4a or 3b=2a, which is same as above. INFORMATION 2 IS SUFFICIENT.
Thus, answer is D i.e. both INFORMATION 1 as well as INFORMATION 2 are sufficient to answer the question.