To earn a 70%, Mike needs to correctly answer 21 questions (70% of 30). So far, he has answered 12 questions correctly (60% of 20).

Therefore, on the last 10 questions he needs  correct answers.

which equals 90%.

For this problem, we must figure out what % alcohol the 10 gallon combined mixture contains.  We know that 4 gallons of 15% alcohol is mixed together with 6 gallons of 45% alcohol.

First we will break down how much alcohol content is within the 4 gallons of 15% alcohol.  .  This means that of the 4 gallons, 0.6 gallons can be considered pure alcohol.

Next, we will break down how much alcohol content is in the 6 gallons of 45% alcohol.  .  This means that of the 6 gallons, 2.7 gallons can be considered pure alcohol.

Therefore, the 10 gallon mixture of both mixtures now contains  of pure alcohol. To find the % alcohol content, we simply divide the amount of pure alcohol by the total volume,  or 33% alcohol.

To solve this problem, we must first add up the ages of all his sons.

. The combined age of his three sons is currently .

The problem states that in , the combined age of the man's three sons will be  of his age.

Therefore we add  to all his sons ages and sum them up once again.

. In , the combined age of his three sons will be .

Now to find what number  is  of, we simply divide  by , . This means that in , the man will be  old. To find how old the man is currently, we simply subtract  from , this means that the man is currently  old.

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

  is 30 percent of 410

 is 25 precent of 480

Quantity A is greater.

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

30 is  percent of 210:

20 is  percent of 160:

Since Quantity A has the smaller denominator with an equivalent numerator, it is the larger value. Quantity A is greater.

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

 is 25 percent of 80:

13 is  percent of 65:

The two quantities are equal.

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: