## September 27, 2003

### Comparisons

Quantitative Comparisons (or QC) comprise of half of the math section.

Remember the answer choices are always the same:
1. Column A is greater than Column B.
2. Column B is greater than Column A.
3. Both columns are equal.
4. The relationship between the columns cannot be determined.

Here are some interesting ones:

 Column A Column B 1. The average (arithmetic mean) of 100, 101, 102. The average (arithmetic mean) of 100, 101, 102. Answer: Choice 3 - Both columns are equal.

Here's another that is similar, but different:
 2. The average (arithmetic mean) of 100, 101, 103. The average (arithmetic mean) of 100, 101, 103. Answer: Choice 1 - Column A is greater than Column B.

 A and B are points on the circumference of a circle. The length of chord AB is 15. 3. Circumference of the circle. 12 Pi. Answer: Choice 1 - Column A is greater than Column B. Since we know the length of the chord is 15, we know that the diameter of the circle is at least 15. The diameter is always the longest chord in a circle. So, the diameter of the circle is 15 or greater.

 The product of two integers is 10. 4. The average (arithmetic mean) of the integers. 3 Answer: Choice 4 - The relationship between the columns cannot be determined. First you man think, {2, 5} and {1, 10} make 10. However, since we're dealing with products, negative numbers can be too {-2, -5} and {-1, -10}. The products of these 4 sets of numbers is 10. But the average isn't always greater than 3.
Posted by oneray at 7:21 AM

## September 26, 2003

### work problems

Here are a few typical work and rate problems for the GRE:

Question 1:
Alice and Bebe can finish a job together in 3 hours. If Bebe can do the job herself in 10 hours, what percent of the job does Alice do?

Let's not use any formulas here. If Bebe can do the job in 10 hours, that means she does 1/10 of the job in 1 hour. We want to know how much work she does in 3 hours, so that's 3/10 of the job in 3 hours. Therefore, Alice does 7/10 of the job in 3 hours (since 10/10 of the job is a entire job). Turn 7/10 into a percentage, and we have 70%. Go Alice!

Question 2:
There are 20 percent part-time employees at Fast Automaton; the rest are full-time employees. At the end of the year 30 percent of the full-time employees received bonuses. If 72 full-time workers received bonuses, how many employees does the Fast Automaton employ?

We know that 20/100 are part-timers and 80/100 are full-timers at Fast Automaton. We also know that 30/100 of the 80/100 employees = 72.
Here are my equations:
0.20W + 0.80W = W
0.30 (0.80W) = 72
Workout the second equation.
.24W = 72
W = 7200/24 = 300
Therefore, Fast Automaton employs 300 people.

Question 3:
Gloria runs from home to the poolhall at an average speed of 6 miles per hour, and then walks home on the same route at an average speed of 3 miles per hour. If her whole journey took one hour, how many miles is her home from the poolhall?

From home to poolhall is 6 m/h and from poolhall to home is 3 m/h. We want to know miles, but we know the total trip was 1 hour.

(X miles) / (6 mph) + (X miles) / (3 mph) = 1 hour
(3X hours + 6X hours) / 18 = 1 hour
(3X + 6X) hours = 1 hour * 18
9X hours = 18 hours
X = 2

Therefore, Gloria's home is 2 miles away from the poolhall.

Posted by oneray at 8:45 AM

## September 22, 2003

### Triangles

Triangles have so many properties. Remember these:
1. Any one side should be less than the sum of the other two.
2. Any one side should be greater than the (positive) difference of the other two.

Special Triangles:
1. 45-45-90: two legs are equal and
hypotenuse = length of leg * square root of 2.

2. 30-60-90: the longer leg = square root of 3 * shorter leg and
hypotenuse = 2 * shorter leg.

Posted by oneray at 9:47 AM

## September 19, 2003

### here goes... something.

Hello. I'm finally doing a blog. Today is the first day at my attempt to share some valuable information with the world.

What kind of useful information can I share with you?

Currently, I'm studying for the GRE. This is my fourth week, and I can already see a dramatic improvement on my quantitative score.

1. Remember, if the question asks: "... which of the following..." review the choices from the bottom up.

2. To calculate work of two people, w = (P * R) / (P + R).

3. Know the properties of triangles.

4. Probability questions appear rarely. If you get one, you know you are doing well!

That's it for today, folks.

Posted by oneray at 10:48 AM