For statement (1), she spent

on rent, and

on clothes.

So she spent  in total.

Therefore, she has  left.

For statement (2), we can set Clara’s salary to be , then we have

Then simplify the equation:

Therefore, .

Now we can just follow what we did for the first statement to calculate the money he had left.

Think of this in terms of "greenhouses per minute", not "minutes per greenhouse". Converting hours and minutes to just minutes, Steve can paint  greenhouses per minute; Phil can paint  greenhouses per minute. 

If we let  be the time in minutes that it takes to paint the greenhouse, then Steve and Phil paint   and  greenhouses, respectively; since one greenhouse total is painted, then we can add the labor and set up this equation:

Simplify and solve:

or 2 hours, 38 minutes.

A work problem is actually a rate problem in disguise.

If you know that an object working alone can do a job in  hours, then you know that the object works at a rate of  jobs per hour. After  hours, the object accomplishes  of a job. Similarly, the other object working alone does a job in  hours, and therefore does  of a job. Together, the objects do one whole job, so solve this equation 

for .

Statement 1 alone gives us half the picture; , but  is unknown.

Statement 2 alone tells us that  is 75% of . But  is unknown.

From Statement 1 and 2 together, we know

 is 75% of  - this allows us to calculate :

75% of  is , so . Since we have both  and , we have the complete equation

and we can calculate .

A work problem is actually a rate problem in disguise.

If you know that an object working alone can do a job in  hours, then you know that the object works at a rate of  jobs per hour. After  hours, the object accomplishes  of a job. Similarly, the other object working alone does a job in  hours, and therefore does  of a job. Together, the objects do one whole job, so solve this equation 

for .

Statement 1 alone tells us that , and Statement 2 alone tells us that .

Therefore, each statement alone gives us only half the picture, but together, they give us the equation

,

which can be solved to yield the answer. 

A work problem is actually a rate problem in disguise.

If you know that David working alone can do a job in  hours, then you know that the object works at a rate of  jobs per hour. After  hours, the object accomplishes  of a job. Similarly, Eddie and Floyd, working without David, do a job in  hours, and therefore does  of a job. Together, the objects do one whole job, so solve this equation 

for .

Statement 1 alone tells us that , and Statement 2 alone tells us that ; each one alone leaves the other value unknown. However, if both statements are given, the equation 

can be solved for  to yield the correct answer.

Since the group is now without the help of Mrs. Smith, we look at Mrs. Smith's contribution to the work as a whole, and the sum of the other two ladies' contribution as a whole; Statement 2, which deals with Mrs. Hume alone, is irrelevant and unhelpful.

Since the three ladies together wrote 400 invitations in 120 minutes, we can infer that they would have spent three-fourths of this time, or 90 minutes, writing 300 invitations.

If Statement 1 is true, then Mrs. Smith, who can write 100 invitations in 90 minutes, would take three times this, or 270 minutes, to write 300 invitations. 

A work problem is a rate problem in disguise. Think in terms of "jobs per hour", and take the reciprocal of each "hours per job". The three ladies together would have done  job in one hour, and Mrs. Smith alone would have done  job in one hour.

Therefore, in one hour today, the two ladies will do

jobs, and in  hours today, they will do

job.

Solve for  in this equation. 

This proves that Statement 1 alone allows us to find the answer - but not Statement 2.

The total time is calculated by the equation . Statement 2 provides the rate, but we have no information regarding distance, therefore, the quesiton is impossible to solve without more information.

The rate formula  - or, actually, the equivalent equation  - will help.

Let  be the speed limits along the interstate, the first half of the state route, and the second half of the state route, respectively.

Then Tom can drive I-10 in  hours; the first half of SR 34, ; the second half of SR 34, .

The time  it takes, in hours, for Tom to make the entire trip is the sum of these fractions: 

.

To calculate , we need . Statement 1 only tells us ; Statement 2 only tells us  and . Therefore, both together, but neither alone, are enough to allow us to calculate .

From the first statement, we can calculate the number of cupcakes Cassie can decorate in 150 minutes. From there, we can calculate the rate at which Derek decorates. Therefore, Statement 1 alone is sufficient to answer the question.

The second statement gives the rate at which Derek decorates cupcakes. Therefore, Statement 2 alone is also sufficient to answer the question.

Statement 1 alone does not tell us enough about the speed of train B to answer the question. Statement 2 alone does not tell us about the rates of either individual train, so it is also not sufficient by itself to answer the question.

But can we figure out the answer using both pieces of information? Yes, we can! If we know that the trains meet at 6:40, then their combined rate of travel is 60 total miles in 40 minutes. Statement 1 says that Train A travels twice as fast as Train B, so we can determine the distances covered by the two trains in those 40 minutes. From there, we can find rates for both trains and then answer the question. Thus, both statements together are sufficient to answer the question, but neither statement alone is sufficient.

Note: We didn't actually answer the question of Train B's arrival time. For data sufficiency questions, don't waste time trying to find the specific answer. All that is necessary is determining whether or not it is POSSIBLE to answer the question with the information given.