Give me any SAT Reasoning Test math question (or a question from a simulated practice test) and I'll post a solution. Specify detail (just the math work or explicit reasoning or w/e) if you want. I'll post ridiculously detailed solutions by default.

#15:
Since OD bisects <AOF, you know that m<AOD = m<DOF, and since you know that OC bisects <AOE, that m<AOB + m<BOC = m<COD + m<DOE, and since OB bisects <AOD, you know that m<BOC + m<COD = x = 40

Now since m<BOC + m<COD = 40, and since we know that OD bisects <AOF, we know that
40 + m<BOC + m<COD = 30 + m<DOE. Substituting, it is easy to see that the expression boils down to 40 + 40 = 30 + m<DOE, which gives that m<DOE is 50.

Finally, we want to find <BOE, which we can do by adding m<BOC + m<COD + m<DOE, which from the information we have derived simplifies to 40 + 50 = 90

#17:
Since we remove every 4 inches, it is useful to find out how many triangles we will remove. This can be found by: 80/4 = 20. Then, notice that for every 1 inch you remove, you gain back 2 inches. So we gain back 20(2-1) = 20 inches, which would make our total length 100 .

You know that the total rope length will be y + 4x, so the insight needed is an expression of y in terms of x. Luckily, we have area which gives xy = 4000. Now, rearranging, we see that x = 4000/y, which we can substitute into our expression to yield 16000/y, choice B

Sum of the arc measures is 2pi or 360 degrees. It's divided into 5 equal segments. ABC gets two of these segments, which leaves 3 of these segments to AEC. Thus ratio of ABC to AEC is 2:3, choice B .

Tom and Bill agreed to race across a 50-foot pool and back again. They started together, but Tom finished 10 feet ahead of Bill. If their rates were constant, and Tom finished the race in 27 seconds, how long did Bill take to finish it?

Tough one. Sounds like an olympiad problem. Not really the intent of the thread, but I'll bite.

The answer is Barbara.

Take a look at it this way: whenever Alan puts some number, n, in an entry in some row, Barbara can just write its negative in the same row. If you continue this process -- since there are an even number of spots -- all the rows will add up to zero so you end up with a matrix that is rank deficient, thus proving Barbara has a winning strategy.

Let P(x) be a polynomial of degree n>1 with integer coefficients, and let k be a positive integer. Consider the polynomial Q(x) = P( P ( ... P(P(x)) ... )), where P occurs k times. Prove that there are at most n integers t such that Q(t)=t.

No that's okay! I'll stop ruining your thread too =p Back to the topic:

If four men need $24 worth of food for a three-day camping trip, how much will two men need for a two-week trip?
I got $56
If it takes 16 faucets 10 hours to fill 8 tubs, how long will it take 12 faucets to fill 9 tubs?
I got 15 hours

16 faucets 10 hours to fill 8 tubs can be reduced to 2 faucets 10 hours hours to fill 1 tub
So, it would take 10/6 hours for 12 faucets to fill 1 tub, and then (5/3)(9) to fill 9 tubs, which gives you the correct answer of 15.

## Replies to: Math help center

#5 pg. 472 of Blue Book

#6 pg. 472 of BB

#8 pg. 473 of BB

1. http://img16.imageshack.us/img16/3329/q34g.jpg

2. http://img193.imageshack.us/img193/9058/78224058.jpg

3. http://img195.imageshack.us/img195/6129/52012792.jpg

Thanks.

Image 1:

#15:

Since OD bisects <AOF, you know that m<AOD = m<DOF, and since you know that OC bisects <AOE, that m<AOB + m<BOC = m<COD + m<DOE, and since OB bisects <AOD, you know that m<BOC + m<COD = x = 40

Now since m<BOC + m<COD = 40, and since we know that OD bisects <AOF, we know that

40 + m<BOC + m<COD = 30 + m<DOE. Substituting, it is easy to see that the expression boils down to 40 + 40 = 30 + m<DOE, which gives that m<DOE is 50.

Finally, we want to find <BOE, which we can do by adding m<BOC + m<COD + m<DOE, which from the information we have derived simplifies to 40 + 50 =

90#17:

Since we remove every 4 inches, it is useful to find out how many triangles we will remove. This can be found by: 80/4 = 20. Then, notice that for every 1 inch you remove, you gain back 2 inches. So we gain back 20(2-1) = 20 inches, which would make our total length

100.#20

You know that the total rope length will be y + 4x, so the insight needed is an expression of y in terms of x. Luckily, we have area which gives xy = 4000. Now, rearranging, we see that x = 4000/y, which we can substitute into our expression to yield 16000/y, choice

B#7

Sum of the arc measures is 2pi or 360 degrees. It's divided into 5 equal segments. ABC gets two of these segments, which leaves 3 of these segments to AEC. Thus ratio of ABC to AEC is 2:3, choice

B.Tom's rate: 100 ft/27 sec

Bill's rate: 90 ft/27 sec.

(27sec/90ft)(100ft) = 30 seconds.

filling entries of an initially empty 2008

The answer is Barbara.

Take a look at it this way: whenever Alan puts some number, n, in an entry in some row, Barbara can just write its negative in the same row. If you continue this process -- since there are an even number of spots -- all the rows will add up to zero so you end up with a matrix that is rank deficient, thus proving Barbara has a winning strategy.

If four men need $24 worth of food for a three-day camping trip, how much will two men need for a two-week trip?

I got $56

If it takes 16 faucets 10 hours to fill 8 tubs, how long will it take 12 faucets to fill 9 tubs?

I got 15 hours

Are these solutions correct?

#1:

Correct.

#2:

16 faucets 10 hours to fill 8 tubs can be reduced to 2 faucets 10 hours hours to fill 1 tub

So, it would take 10/6 hours for 12 faucets to fill 1 tub, and then (5/3)(9) to fill 9 tubs, which gives you the correct answer of 15.