It can help to begin by writing the expression using scientific notation:

Now remove common divisors from the numerator and denominator:

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively.  Therefore, the only answer which is within the desired range is 2/5.

Looking at the differences in prices, one might guess that Quantity B is the answer. Beware the easy answer; always check.

Instead, calculating how many cases of claws Vega can buy, keeping in mind that he cannot purchase part of a case. Do not round up!

Quantity A:

Quantity B:

In either case, he can buy no more than seventeen cases. The two quantities are equal.

Looking at how close the dollar values are for A and B, it's tempting to think the GRE is being tricky, and that B will allow for the purchase of more cases of seeds.

Do not assume; check to see whether or not this is the situation. Note that a portion of a case cannot be purchased; round down to the nearest integer when calculating how many cases may be bought.

Since each case is $343.25

Quantity A:

Quantity B:

The two quantities are equal.

To convert a fraction into a decimal, you simply need to divide the numerator by the denominator.  When the problem prompts you to round to the nearest thousandth, that means that you round to the third decimal place (i.e. go to the third decimal place, if the fourth is four or lower, you can leave the third decimal place digit alone, if the fourth is five or higher, raise the third decimal place digit by one). 

When you divide 16 by 17 you will need to add a zero and a decimal place to 16 making it 160. From here we see that

 but since we added a decimal place to 16 to create 160 we now need to move the decimal place of the answer one unit to the left.

The first step will be to calculate how many total different potential rolls are possible. This is given by the product of the number of possible rolls for each of the dice: 6, 6, 20:

Next it is necessary to account for the total number of rolls that will sum up to 5. Writing them out can help, such as in the format of:

Knowing that there are 6 different rolls that sum up to 5, the probability of rolling a 5 can be found by taking the number of events that satisfy this sum and dividing it by the number of total possible events:

Looking at this equation, note that since all terms in the numerator and denominator contain a , it is possible to rewrite it as follows:

or

Now the parenthetical terms must be addressed. The problem statement and answer choices give a clue that they are some sort of multiples of .

In fact, Pascal's triangle reveals that the top and bottom are the cube and square of this term respectively:

Cancelling terms, we are left with:

Examination of the value  reveals that after the sequence , the decimal repeats, and that the sequence has a length of eight values.

A longer answer would be to write the sequence out and count down the digits until the  value was found. However, this is a time-consuming process and one that is prone to error.

Rather, notice how since the numbers repeat, it's possible to skip most of the counting:

 digit: 

 digit: 

And so on. Since  is the closest multiple to , we can subtract the two to find the digit that matches the  digit.

So the  digit is .

The first step will be to find the reciprocal of  percent. Note that as a percent, this should be converted to a decimal form: .

The reciprocal of a number is given by  divided by that number, so the reciprocal of  is given as:

Therefore:

To make the comparison, the values of  and  must be determined.

We are told that  percent of  is , so its value can be determined as follows:

With  known, it is possible to find , since  percent of  is :

The two quantities are equal.