Since the starting number is a mixed number fraction, the decimal number must also have a value in the ones place. Since the denominator in the fraction has a value that is a factor of , both the numerator and denominator can be multiplied by a factor of  to form  tenths. (Note, the first decimal place value is the tenths place).

The key to this problem is to realize that the store cannot buy partial crates of wristbands--it's all or nothing. Calculate how many crates can be bought with each sum of money by dividing the sum by the price of a crate.

Quantity A:

Although oh so close, only eight crates can be bought with this sum of money. Don't round up!

Quantity B:

There's just enough to buy nine crates.

Quantity B is greater.

To begin with, it is easiest just to add these decimals together using your calculator:

Now, this is the same thing as:

We can rewrite this:

To find this, you need to give the two numbers a common denominator:

This is your answer.

In decimal form  is said 33 hundredths.

This is equal to

.

This fraction cannot be reduced any further therefore it is in its final answer form.

To convert a decimal into a fraction, simply put the digits of the decimal in the numerator of a fraction, then one followed by a number of zeroes equal to the number of digits in the decimal as your denomator.  In this case:

Then, you can simplify, as both  and  are divisible by :

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.