Fractions - GRE Quantitative Reasoning

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting . Next, you add this to the numerator of your fraction, giving you , or . Finally, you place this over your original denominator, giving you:

The arithmetic mean of a set is defined as the sum of terms in the set divided by the number of terms of a set. Therefore, the mean for this problem can be found as:

The average, or arithmetic mean, of a set can be found by dividing the sum of the set by the amount of values in the set:

The median for a set depends on if there's an even or odd number of values in the set.

For an odd number of values in a set that is arranged in numerical order, , the median is given as the middle value, .

For an even number of values in a set that is again arranged in numerical order, ,there is no value exactly in the middle; rather there are two. The median is then given as the average of these two values:

Rearranging the set into numerical order gives , thus the median is

To find the part from the whole, just take the percentage and turn it into an algebra problem.

In decimal form, 20% is .2. To turn it into an equation, recognize that "is" means equal to and "of" means multiply.

Therefore, "17% of 325" becomes (.17)(325) = X.

A way of solving this without a calculator:

10% of 325 is easy to find: 32.5.

20% will be twice as much as 10%, so 65.

1% is easy to find: 3.25.

3% is three times 1%: 9.75.

20% – 3% = 17%

65 – 9.75 = 55.25

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.

With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:

Now we can see that the equation can all be divided by y, leaving the answer to be:

_x_2 – _y_2 can be also expressed as (x + y)(x – y).

Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).

This simplifies to (x – y).

Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.

125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.

120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.

Set up the conversions as fractions and solve:

To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

Factor both the numerator and the denominator:

After reducing the fraction, all that remains is:

Notice that the term appears frequently. Let's try to factor that out:

Now multiply both the numerator and denominator by the conjugate of the denominator:

The numerator and denominator are both divisible by 12. Thus, we divide both by 12 to get our final answer.

If we instead divide by another common factor, we may need to complete the process again to make sure that we have completely reduced the fraction.

In mathematical words we get the following:

This can be solved using 2 methods.

The most time-efficient solution would recognize that is the largest value and nearly equals the sum the other fraction by itself.

The more time consuming method would be to convert each fraction to decimal form and calculate the sum of each quantity.

Quantity A:

Quantity B:

When we factor the numerator and denominator, we get:

.

After cancelling , we are left with .

With common denominators, the range is from

or

.

The only fraction that falls in either of these ranges is .

2/5% = 0.40% = 0.004. Therefore, Column B is greater.