Firstly, we should remember that the average rate is given by the following formula , where  is the total distance and  is the total time. So to answer this question we should find a value for .  can only be found by adding the two times for both trips. By pluging in the values we can find a value for , therefore we need  both statements.

To solve this problem, we need to find the rate of the train considering the fact that the rails are damaged. The first statement tells us only the usual rate of the train and is therefore not sufficient because we don't know how fast the train will be going on the damaged portions of the railroad. 

Statement two only tells us that the train must progress at a rate half as slow as its usual rate. 

Using statements 1 and 2 we can easily find the rate which is given by . Note that this rate is given in miles per minutes but we don't have to calculate it, we just need to know that we can calculate it.

Since we are told an average speed for a round trip we should be able to set the following equation , where  is the distance of a one way and  is the total time of the round trip and  is the average speed of the plane.

Statement 1 tells us that it took the plane twice as long to do the first portion of the round trip, therefore we can figure out  from this statement, indeed,  where  is the time it took to do the second portion of the trip. Therefore, . Since  is the rate for the second portion of the trip, we can figure it out by pluging in the values , which is  sufficient to answer the problem.

Statement 2 tells us that the plane was flying at a speed of , this alone answers the question.

For these types of problems, asking us how long it takes for a vehicle to catch up to another one, we should keep in mind that we can calculate the rate at which the other vehicle is catching up, by doing the difference of the two rates.

From this we can see that we will need both rates for the vehicles as well as the distance between the two vehicles: , where and are the respective rates of vehicles B and A, and  is the distance between the two cars and  is the time it would take for car B to catch up

Statement 1 only tells us the distance between the two vehicle and therefore we don't know how fast car B is catching up and therefore this statement alone is insufficient.

Statement 2 only tells us how fast is the second car going, but here we don't know what is the distance between the two cars.

Therefore, both statements must be taken together to answer this question.

First of all, we should notice that we are looking for a rate and therefore, we should be able to find both a distance and a time for the train to travel that distance.

From statement 1, we can say that  and that  where  is train A's rate and  is the time it takes train B to travel 180 miles. If we manipulate our equations we get : , since 180 are in both equations. But there are two unknowns and neither cancel out. So statement 1 alone is not sufficient.

Statement 2 gives us a rate for train A for an unknown distance, therefore this information is not useful. 

We can see that after using our statements, even together, we still could not find an answer to the problem, therefore statements 1 and 2 together are insufficient.

From statement (1), we can get the annual interest rate:

.

Therefore after year 2 the simple interest is:

. So statement (1) alone is sufficient.

Statement (2) gives us the annual interest rate directly so we can get the result by simply applying the simple interest formula:

. So statement (2) alone is sufficient.

Therefore the right answer is D.

Statement (1) is not very helpful. Since we do not know the total amount of interest earned or at least the interest earned from one of the financial products (either the bonds or the certificates), we cannot determine the original amount invested in either product.

Using Statement(2), we can set the following equation:

(Let x be the amount invested in bonds)

John invested $4200 in bonds and $7800 in certificates.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

(1) The amount of interest earned on this investment in one year is $400.

  Let X be the amount invested. The simple annual interest rate is 8%.

The amount of money John invested is $5000. Statement (1) Alone is sufficient.

(2) John's investment is supposed to accumulate to 7,000 after 5 years.

  Let X be the amount invested. The simple annual interest rate is 8%.

The amount of money John invested is $5000. Statement (2) Alone is sufficient.

Simple interest can be calculated using the formula

where  is the principal, or amount deposited;  is the interest rate, expressed as a decimal; and  is the time, expressed in years.

The question is whether the total of the original principal and the accrued interest will be at least $10,000, or, whether

or

is true or false.

Assume both statements. From Statement 1, we get that , and from Statement 2, we get that . However, neither statement gives the value of principal , so the two statements together are insufficient to answer the question.

Simple interest can be calculated using the formula

where  is the principal, or amount deposited;  is the interest rate, expressed as a decimal; and  is the time, expressed in years. Since the main body of the problem gives that Grant deposited $5,000 and that the amount of interest to be earned is 

,

the equation becomes 

Therefore, all that is needed to calculate  is the interest rate of the account. Statement 1 gives this explicitly. Statement 2 is irrelevant, as it only compares the interest rate to that of another account, which is not given.