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.

Assume both statements together. If we let  be the interest rate, as a decimal, for Grace's account, the amount of interest Grace's account accrues over five years is

The interest rate of Shannon's account is , so, if we let  be amount she deposited in her account, the amount of interest Shannon's account accrued is

Without any information about how much Shannon deposited, or about the actual interest rates, it is impossible to determine which is the greater.

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, expresssed in years. For both accounts, , so the amount of interest earned will be

Neither statement alone gives sufficient information; Statement 1 alone compares the interest rates but not the amounts of principal, and the reverse holds true for Statement 2. 

Assume both statements. The accounts pay the same interest rate, which we will continue to call ; however, the principal Robin deposited, which we will call , is greater than that deposited by Rick, which we will call . Therefore,

That is, Robin's account accrues more interest.

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. Since this makes , the question becomes whether

or

is true or false.

Statement 1 and Statement 2 each give the value of only one of the two variables—Statement 1 gives that  and Statement 2 gives that —but neither gives the other value. The two together, however, allow us to substitute for both variables and test the inequality for truth:

This statement is true, so the savings account will indeed accrue to a value above $10,000 by Marshall's 21st birthday.