To attempt this problem, translate the statements into mathematical equations.  When you see the word 'is', it very often means 'equals:

 is  percent of :

Now before we continue, look at this statement. We see that s is fourth fifths of r. That alone should tell us that r is greater!  However, we can continue with the calculations to see what these values are, if only for the sake of robustness. However, on the GRE, once you find the answer like this, fill it in and move on.

 is  percent of 

Again, this validates our result. We may not know what r and s are, but we know how they relate to each other, and that is enough.

Quantity B is greater.

To solve this problem, translate  is what percent of  into mathematical terms:

All of the answer choices are above $20,000, so assume that Donny paid the 6% on that:

That means of the $2,000 he paid in taxes

$800 was taken from any income he made above the $20,000 line, and was thus taxed at 10%:

Donny's income must therefore have been

Begin by finding out how many of the 20 professors are male:

That means that there are eight males and twelve females currently to sum up to twenty.

Now, two males and two females leave, meaning the faculty is reduced by four:

The amount of males has been reduced by two:

Therefore, the percentage of the faculty that is male can be found as the number of males divided by the total faculty size times 100:

12% of 15,000 is 0.12 * 15,000 = 1800.

8% of 15,000 is 0.08 * 15,000 = 1200; therefore in total, Mary spent 1800 + 1200 = $3000 more.

Divide Mr. Day's salary by 165 to determine how much the school pays him per day: Mr. Day makes $149 per day.  They only have to pay substitute $90 per day, saving them $59 per day. To figure out how my they save totally, multiply by 5 to get how much they save for the week Mr. Day is sick: $295. 

To find the profit percentage, you must first determine the amount of profit made on this transaction.  If the sale price was $20 and the production cost $17.50, then the profit made was: 20 -17.5 = $2.50.  The profit percentage is determined by dividing the amount of profit made by the original price, or 2.5 / 17.5 = (approx.) 0.14286 or 14.29%.

Begin by translating your problem into an equation.  What we want to ascertain is the situation when the profit equals exactly 0.  The profit and loss for a given month can be summarized by the following equation:

(Total product revenue) - (Base operating costs) - (Individual costs for products) = 0

Given our data, we can rewrite this:

15 * x - 30,000 - 5 * x = 0

Combine like terms:

10 * x - 30,000 = 0

Isolate x:

10 * x = 30,000; x = 3,000.

Therefore, the manufacturer must sell at least 3,000 items per month in order to "break even."

First, we must ascertain the original profit.  Per shirt, the retailer made 15 – 8, or $7.  Selling 300 shirts, it made a profit of $2,100.

The new price, discounted by 20% is equal to 80% of the original price, or 15 * 0.8 = $12.  This yields a profit of $4 per shirt.

To ascertain the number of sales needed to make $2,100 in profit, we must solve the following equation:

4x = 2100; x = 525 shirts

The amount of profit made on the item is 578 – 235 = $343. This is 343/235 or (approximately) 1.4596, which is 145.96% of the original price.