To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:

Either way, you can now find the tax rate:

Each statement has enough information to calculate the answer. 

Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let  be the total price of jewelry sold last month. Then,

 so

Increasing that by 25% we see that

NOTE: when multiplying the percents, make sure you use the decimal values.

Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let  equal the total price of jewelry sold this month, we get 

or

Therefore we see we can use either statement individually to find what we are looking for. 

First let's find the number of chairs not delivered:

Therefore the fraction of chairs not delivered is .

Divide the numerator by the denominator to convert this fraction into a decimal:

Multiply by 100 to turn this decimal into a percentage:

Statement (1) indicates the percentage of women who do not have a college degree. From that statement, we know that 60% of the women in the company have a college degree. However, we do not know the total number of employees or the total number of women in the company. Therefore, statement (1) alone is not sufficient.

Statement (2) indicates the percentage of men who have a college degree but from that statement we cannot find the total number of employees or the total number of women with a college degree.

We need the total number of women and the total number of employees in order to calculate the percentage of employees who are women with a college degree. We show it with the following example:

If we assume that there are 100 women and 100 men working in the company, we can attempt to find the percentage of employees who are women with a college degree in the following way:

So in that example, 30% of the employees are women with a college degree.

However if we change the number of women to 500 and the number of men to 600, the percentage of employees who are women with a college degree is:

The percentage of employees who are women with a college degree becomes 25%.

Therefore both statements together are not sufficient.

Statement 1 alone is inconclusive. For example, if , then  is 30% of 10 - that is,

,

an integer.

But if , then  is 30% of 15 - that is,

,

not an integer.

If Statement 2 alone is assumed, then  for some integer . 60% of this is 

.

 is three times an integer and is itself an integer.

Assume Statement 1 alone. 

If  is 30% of  and  is 30% of , then:

and

or

 is an integer; for  to be an integer,  must be divisible by 100. This makes Statement 2 a consequence of Statement 1, so we can now test Statement 2 alone.

If  is divisible by 100, then for some integer , . 30% of this is .  is 30 times some integer, and is therefore an integer itself.

Either statement alone answers the question.

Assume both statements are true. 

Case 1: . 

Then  is 20% of this, so 

 is 20% of , so

Case 2: 

Then  is 20% of this, so 

 is 20% of , so

In both situations, the conditions of the problem, as well as both statements, are true, but in one case,  is not an integer and in the other case,  is an integer. The statements together are inconclusive.

 is 25% of , so

.

Similarly, .

Therefore, 

,

or, equivalently,

or

.

If  is an integer, then 16 is a factor of . This contradicts both Statement 1, since 16 is composite, making  composite, and Statement 2, since this makes  a multiple of  - that is, even. Either statement alone answers the question in the negative.

 is 60% of , meaning that , or, equivalently, .

From Statement 1 alone, since , it follows that

This is enough to prove that .

 is 60% of , so .

From Statement 2 alone, since , it follows that 

.

This is enough to prove that .

For one candidate to have won the election outright, (s)he must win more than 50% of the votes. 

Statement 1 alone does not prove there was an outright winner. For example, if Rodger got 211 votes, then Stephanie got 111 votes, and Tina got 1 vote; this makes Rodger's share of the votes 

,

making Rodger the outright winner. But if Rodger got 500 votes, then Stephanie got 400 votes, and Tina got 290; Rodger got the most votes, but his share is

,

not the required share of the vote.

Statement 2 alone does not prove this either, since 74.1% of the vote was won by either Rodger or Stephanie, but it is not specified how this is distributed; Roger or Stephanie could have won 51%, with the remaining 23.1% won by the other, resulting in an outright winner. However, it is also possible that each won half this, or about 37%, resulting in a runoff between the two.

Now assume both statements are true. Let  be the number of votes won by Tina. Then Rodger won  votes and Stephanie won , or , votes. The total votes are 

.

Since Tina won 25.9% of the vote, we can set up an equation:

This can be solved for . From this, the number of votes each candidate got, the votes cast, and, finally, the percent of the vote each won can be calculated.