Arithmetic - GRE Quantitative Reasoning

First count the total number of parts in the ratio.

Then we can set up a proportion representing .

As the initial ratio shows, there are 6 pennies for every 14 total coins. In the total set, we have X pennies and 42 total coins. Plugging these numbers into the proportion gives .

Finally, we multiply both sides times 42 to isolate x.

2 gallons of lemonade equals 8 quarts of lemonade. To make 3 quarts of lemonade, you need of the amount needed to make 2 gallons of lemonade, or 6 ounces of mix.

When converting percents into decimals, know that the tens and ones digit of the percent will occupy the tenths and hundredths places of the decimal. Any decimal following the whole percent will follow in sequence (i.e. the first decimal place in a percent corresponds to the thousandth place, and so on). Therefore, ninety-seven point five percent is equal to:

To convert a percentage into a decimal, simply place the decimal point in front of the tens digit of the percentage. So, % becomes .

To convert a percent into a decimal, simply know that the tenths place of the decimal will correspond to the tens digit of the percent, and the thousandths place of the decimal will correspond to the ones digit of the percent. Any ensuing digits will be behind a decimal in the final percent.

Also converting a decimal to a percent can be accomplished by multiplying the percent by 100.

Therefore, the best answer here is:

To express a decimal as a percent, multiply the decimal by one hundred:

Then add your percent sign after:

To express a decimal as a percent, multiply the decimal by one hundred:

Then add your percent sign:

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 .