(1) The total amount of interest earned on all investments at the end of one year is $800.

Let A be the amount of money invested at x percent. The total interest earned on both investments is:

We cannot calculate A because x is also unknown. Statement (1) Alone is not sufficient then.

(2) x=6%

Statement (2) Alone is not sufficient.

Combining both statements, we have:

Both Statements together are sufficient but neither statement alone is sufficient.

Using statement (1), the value of i cannot be determined because t is not specified.

Therefore Statement (1) ALONE is not sufficient.

Using statement (2), the value of i can be determined:

We can then set the following equation with X being the amount of money Jenna has to invest today:

We calculate X as follows:

The compound interest equation is

where  is the value at the end of the period in question,  is the principal, or initial investment,  is the interest rate in decimal form,  is the number of times the interest is compounded per year, and  is the number of years. 

We know  from the main body of the problem. It is known that   only if Statement 1 is knwon, and it is known that  only if Statement 2 is known. Also,  can only be deduced from Statement 2:

Therefore, neither statement alone is sufficient. If both statements are assumed true, the equation becomes 

or, dividing both sides by 20,000,

The question can be answered by substituting 4 (quarterly), 6 (bimonthly), and 12 (monthly) in turn and seeing which one makes the above statement true.

Assume Statement 1 alone is true.

If  is the annual interest rate, in its decimal form, of a $4,000 CD that draws $7.83 interest in the first month, then

This is a linear equation in one variable that can be solved for .

Assume Statement 2 is true. Then the equation becomes

This is a quadratic equation in one variable that can be solved for .

Either way, the annual interest rate can be found, so either statement alone is sufficient.

The two statements are equivalent, since 0.964% of $30,000 is 

Therefore, it can be determined that the interest rate 0.964% is per compounding period. However, no clue is given as to how many compounding periods there are - for example, the annual interest rate is unknown. The two statements together provide insufficient information.

In order to know how much money is in an account after compound interest is accrued, one thing that must be known is the principal, or amount invested.

Statement 2 is unhelpful, since information from 2013 is not relevant to information for 2014. 

From Statement 1 we only know her 2014 earnings, not her December earnings (it is not given that she earned the same per month in 2014). Therefore, the two statements together provide insufficient information.

In order to know how much money is in an account after compound interest is accrued, the following must be known:

The amount of principal, which is given as $3,000 (Natasha's Christmas bonus) only in Statement 1;

The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;

The frequency with which the interest is compounded, which is given as monthly in the main body of the problem; and,

The rate of interest, which is given as 2.15% in the main body of the problem.

Statement 1 alone provides sufficient information to allow the answer to be calculated. Statement 2 is irrelevant, since it provides no information about Natasha's Christmas bonus.

In order to know how much money is in an account after compound interest is accrued, the following must be known:

The amount of principal, which is given as $10,000 only in Statement 1;

The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;

The frequency with which the interest is compounded, which is given as quarterly only in Statement 2; and,

The rate of interest, which is given as 2.12% only in Statement 2.

Therefore, both statements together are necessary and sufficient to answer the question.

Assume both statements are known.

In order to know how much money is in an account after compound interest is accrued, the following must be known:

The amount of principal, which is stated to be $5,000 in Statement 1;

The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;

The frequency with which the interest is compounded, which is given to be monthly in Statement 2; and,

The rate of interest, which is not given anywhere.

Insufficient information is given.

This is a binomial probability experiment. 

The probability that a fair coin will come up heads in any single toss is . 

If the coin is tossed four times, then the probability that heads will appear three times is:

The probability that heads will appear four times is:

So the probability that heads will appear at least three times is 

The second statement is irrelevant; the result of a previous trial has no influence on that of the current trial. It has already been established in the problem that the coin is fair.

The answer is that Statement 1 alone is sufficient to answer the question, but not Statement 2.