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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Thank you that clears it up, I was timing myself so trying to get through the problem in 2min or less. When I read the two statements I came to the exact same conclusion you did on statement 1; I can determine exactly how many bottles machine X made, but I don't know how many bottles = 1 lot, Insufficient.

However in reading statement 2 I felt it wasn't enough to answer the question by itself (Machine X produced twice as many bottles as Y) I didn't have a rate or a total, However, from statement 1, I could get an exact answer of how many Machine X produced, then simply divide by 2 to get the amount Machine Y produced. Adding these two together will give me the total bottles in one lot. With both statements I have all the information I need to determine how long it would take Machine X to fill the lot by itself because now I have it's rate and the total number of bottles in one lot. So I chose "C" Both statements together are sufficient

How could this logic be wrong?
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There are several important things you should know to solve work problems:

1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance <--> time*rate=job \ done. For example when we are told that a man can do a certain job in 3 hours we can write: 3*rate=1 --> rate=\frac{1}{3} job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then 5*(2*rate)=1 --> so rate of 1 printer is rate=\frac{1}{10} job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then 3*(2*rate)=12 --> so rate of 1 printer is rate=2 pages per hour;

So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job --> 1/6 of the job will be done in 1 hour (rate).

2. We can sum the rates.

If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is rate_a=\frac{job}{time}=\frac{1}{2} job/hour and B's rate is rate_b=\frac{job}{time}=\frac{1}{3} job/hour. Combined rate of A and B working simultaneously would be rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6} job/hour, which means that they will complete \frac{5}{6} job in one hour working together.

3. For multiple entities: \frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}, where T is time needed for these entities to complete a given job working simultaneously.

For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;

Then: \frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}, where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that t_1 and t_2 are the respective individual times needed for A and B workers (pumps, ...) to complete the job, then time needed for A and B working simultaneously to complete the job equals to T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2} hours, which is reciprocal of the sum of their respective rates (\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3} hours.

BACK TO THE ORIGINAL QUESTION:
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?

You can solve this question as Karishma proposed in her post above or algebraically:

Let the rate of X be x bottle/hour and the rate of Y y bottle/hour.
Given: 4x+3y=job. Question: t_x=\frac{job}{rate}=\frac{job}{x}=?

(1) Machine X produced 30 bottles per minute --> x=30*60=1800 bottle/hour, insufficient as we don't know how many bottles is in 1 lot (job).
(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours --> 4x=2*3y, so 3y=2x --> 4x+3y=4x+2x=6x=job --> t_x=\frac{job}{rate}=\frac{job}{x}=\frac{6x}{x}=6 hours. Sufficient.

Answer: B.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
questions-from-gmat-prep-practice-exam-please-help-93632.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done
hours-to-type-pages-102407.html?hilit=answer%20choices%20or%20solve%20quadratic%20equation.%20R

Hope it helps.
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1) does not tell us anything about Y. INSUFFICIENT

2) machine X produced twice as much as Y did i.e. did \frac{2}{3} of the work.

\frac{2}{3} work required 4 hours

1 complete work requires \frac{4*3}{2} = 6 hours

Answer: B

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