The best approach to this equation is to evaluate each of the equations and inequalities.  The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.

¹/₂ is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.

√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.

Finally, the fraction ¹/₃ has repeating 3s which makes it larger than ³/₁₀ so it is true.

To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.

4/10 = 0.4

4/15 = 0.267

So the possible values for m are 0.267 < m < 0.4

Now let's find the value for 7/13, to make comparison easier.

7/13 = 0.538

Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.

The GRE test now has a built-in calculator.  Simply convert the fractions to decimals and compare:

Quantity A = 0.333 +0.43 + 0.2 = 0.963

Quantity B = 0.1429 + 0.5 + 0.3333 = 0.976

Thus, Quantity B is larger.

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666...  0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20  and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

To solve this problem, simply divide the numerator by the denomenator. We see that when we try to divide these two numbers that 9 does not go into 2 therefore we need to add a decimal place and a zero to 2. Now we have 2.0 divided by 9 from here we can see that .2 times 9 gives us 1.8 which is close to 2. Now we subtract 1.8 from 2 and are left with .2. We repeat this process.

You are left with  repeating, which can be rounded to , so that is the best answer. 

To express a fraction as a decimal, simply divide the numerator by the denomenator.  In this case, you divide thirty two by thirty seven. From here add a decimal place and a zero after 32. Now we are able to divide.

Thus yielding:  repeating.  

Round to the nearest hundredth, and you get  because the value in the thousandths place is a four or lower therefore, the value in the hundredths place remains the same.

To convert, first divide the numerator by the denomenator. For this problem we will need to add a decimal place and a zero to the end of 17 before we divide.

Then, you will yield  repeating.  

Then you can round to the nearest hundredth, which will give you your final answer of .

Since the value in the thousandths place is a seven which is greater than four, we will need to round the value in the hundredths place up to eight.