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OG-12 Question

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OG-12 Question

by parulmahajan89 » Tue Aug 14, 2012 11:04 am
112. Machines X and Y produced identical bottles at
different constant rates. Machine X, operating alone for
4 hours, fi lled part of a production lot; then Machine Y,
operating alone for 3 hours, fi lled the rest of this lot.
How many hours would it have taken Machine X
operating alone to fi ll 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

I just want to know what would be quickest way to solve this problem?

Thank you
Parul Mahajan
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Source: — Data Sufficiency |
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by msbelasco » Tue Aug 14, 2012 12:51 pm
Ok, so what we know from the statement alone is as follows.

-Machine x produces a certain amount of the lot in 4 hours

-Machine Y does the rest in 3 hours

-The question wants to know how many hours machine x will take to do the whole thing alone.

(st. 1) - this statement only tells us how many bottles x produces, but nothing about the total order or about machine y. So we can eliminate this as being the sole answer

So, we can move on to statement 2 and temporarily ignore statement 1

(st 2) now this gives us a relation between the two machines, and from the original statement we know that the order is completed between the two machines in this amount of time.

So machine X produces 2 times the amount in 4 hours as machine y does in 3 hours. Let's plug in fictitious numbers to get a relation between the two. It is a good idea to use a number you know will be able to be divided by all the numbers present in the equation (i.e. 3,4,2).

So let's say machine x produces 24 bottles in 4 hrs and machine y produces 12 in 3 hours. So we know the total order in this case is 36, so how long will it take machine x to make 36 bottles?

Divide 24 by 4 (4 hours to make 24 bottles), to get 6 bottles per hour. 36 bottles divided by 6 bottles per hour = 6 hours.

So B is sufficient.

You don't need to actually do the equation, but as soon as you realize that it can be done, you can choose it as the answer
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