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You're using the complement rule. Let E be some event. P(E) = 1 - P(complement of E) The complement of E contains everything in the sample space that is NOT E. In your example, the sample space is: neither of the two are lawyers, exactly one of the two are lawyers, and both are lawyers. Also, E is the event that neither are lawyers. If we want P(neither), then we need 1 - P(complement of neither). In this case, P(complement of neither) = P(exactly one) + P(both). See this for more information: Complement of an Event.

P(Neither) = 1 - P(Both) - P(Exactly One) You forgot the exactly one part.

Thanks for the helpful responses so far. Ok, now say you have a graph like the attached. What's to quickest way to solve the following question? This is from Princeton Review. In 1970, for which of the following motion picture studios was the ratio of ticket sales to advertising expendires lowest? Answer:

Let's say you're faced with a bar graph like the following, but with more difficult numbers. http://www.basic-mathematics.com/images/double-bar-graphs1.gif You want to see which student has the lowest ratio of Test to Pretest scores (again, just an example). What's the best way to compare the ratios?

For the one with O is the center of the circle, the distance between P and Q is 4, draw a circle on a piece of paper. Label the top-most point as R. Draw in OP. You know that OP is 2 and so is OR. This means that the triangle that you just constructed (OPR) is isosceles. Therefore, angle OPR is 35. Since the sum of the angles of a triangle is 180, you know that angle POR is 110. This implies that y is 70, since PQ is the diameter of the circle (and thus is a straight line). If PQ were not the diameter, the distance between P and Q would not be 4. For the raspberry, strawberry, and blueberry one, draw a Venn diagram with three circles and fill in the numbers that you know (the problem gives you four that you can directly fill in). Then, label the regions you don't know as A, B, and C. Based on the total number who like raspberries, strawberries, and blueberries, you can form three equations in three unknowns. Solve for the letter where only strawberries and blueberries overlap and you'll get 21.

Those answers are the same (but, yes, they do look different). :)

First off, fantastic score. Congratulations! I'm wondering if you can expand on this point a bit more. How did the difficulty of the quantitative section on the actual test compare to the difficulty of the quantitative section on the Barron's model tests?

Yes. I think I edited my post after you saw it.

#1. Amount budgeted for the environment: 6.9 (from the pie chart) Amount allocated to national parks: (1/3)(6.9) = 2.3 Amount allocated to other environmental areas: 6.9 - 2.3 = 4.6 #2. You are correct. Alternatively, you can assume that there are 100 people polled and go from there.

I got a different answer than the above. We can get a sum of 1 in each of (-9 + 10), (-11 + 12), and so on. There are 13 such pairs (the first 26 terms of the sequence). The last term of the sequence is -35. Thus we have -35 + 13 = -22. So, I get that they're equal.

Think about it this way. We have a job to do: we need to place integers (numbers) into the thousands, hundreds, tens, and ones place to create a four-digit number according to the criteria specified. We can place only 5 numbers into the thousands place: 1, 3, 5, 7, 9 (these are the odd numbers at the beginning). We can place any number we want into the hundreds place (0-9) and we can do that again for the tens place (0-9). There are 10 possible numbers for each case. Finally, we can place only 5 numbers into the ones place: 0, 2, 4, 6, 8 (these are the even numbers at the end). By the counting principle, we can simply multiply each together. See Fundamental counting principle for more.

1) See http://www.www.urch.com/forums/gre-math/132590-average-speed.html#post863585 2) The triangles are only similar, not congruent. You can draw one VERY big and the other VERY small (and vice versa)--just for the sake of argument. So, the relationship cannot be determined. 3) Let one circle have radius 1 and the other have radius 2. Large circle area = 4pi, small circle area = pi, area of the shaded region = 4pi - pi = 3pi. Choosing a point at random we have a 3pi/4pi = 3/4 chance of getting in the shaded region. In other words, the shaded region is 3/4 of the area of the big circle. 4) We have 3*5*7*11 = 1155, so they're equal. We need four distinct prime factors greater than 2 and these are the smallest four that satisfy the given criteria. 5) We have 5 choices for the thousand place, 10 for the hundreds, 10 for the tens, and 5 choices for the last digit. By the counting principle, we have 5*10*10*5 = 2500.

You should take the weighted average of the speed. Since there's no information regarding units, I'll assume you want km/hr. FIRST TEN MINUTES: 1 km/min or 60 km/hr SECOND TEN MINUTES: 3/2 km/min or 90 km/hr Here's the weighted average. (10 minutes = 1/2*(20 minutes)) (1/2)(60) + (1/2)(90) = 30 + 45 = 75 km/hr.

The answer is undoubtedly B. I don't know where this question came from.

Just list the cases. We need X to be even. If X is odd, then X+Y is odd, so X+Y can't be 24. Thus, we have X = 3 pts 0 (remember, 0 is even!), 6, 12, 18, 24. Therefore, t can have FIVE values, or (B). There's an error in this problem. (E) should be 15, not 415. Pick a nice number for n, say 3. Then each floor has 6 apartments. On each floor, we take 2 apartments and make one bigger one out of it. This leaves us with 9 floors and 5 apartments per each floor. This is 45, or 15n = 15(3) = 45 apartments total. Choice (E) is the answer.