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Math help center

ArachnotronArachnotron 1658 replies103 threads Senior Member
edited December 2013 in SAT Preparation
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.
edited December 2013
312 replies
Post edited by Arachnotron on
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Replies to: Math help center

  • Vertigo220hVertigo220h 815 replies99 threads Member
    Umm..
    #5 pg. 472 of Blue Book
    #6 pg. 472 of BB
    #8 pg. 473 of BB
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    Harambee:

    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 .
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    Image 2:

    #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
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    Image 3:

    #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 .
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  • HarambeeHarambee 2600 replies4 threads Senior Member
    Thanks! Much appreciated.
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    Anytime. I enjoy these problems, so I figured I'd help you all out :)
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    @Vertigo220h: please type up the questions. I've long since discarded my blue book.
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  • anhtimmyanhtimmy 3168 replies89 threads Senior Member
    what is 2 + 2? I seem to be baffled by this question!
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    Well, it depends. In base >= 4, 2+2 = 4. In base 1, the question is illogical. In base 2, the question is illogical. In base 3, it is 11.
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  • anhtimmyanhtimmy 3168 replies89 threads Senior Member
    Makes perfect sense! Thank you sensei
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    Indeed. 'tis my job to be familiar with tricky questions like the one you posed.
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  • GREGRE 26 replies7 threads Junior Member
    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?
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    GRE:

    Tom's rate: 100 ft/27 sec

    Bill's rate: 90 ft/27 sec.

    (27sec/90ft)(100ft) = 30 seconds.
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  • GREGRE 26 replies7 threads Junior Member
    Alan and Barbara play a game in which they take turns
    filling entries of an initially empty 2008
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    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.
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  • GREGRE 26 replies7 threads Junior Member
    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.
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    This one is...significantly more difficult. I can message you my attempts at a solution if you'd like, once I've made some progress.
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  • GREGRE 26 replies7 threads Junior Member
    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

    Are these solutions correct?
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  • ArachnotronArachnotron 1658 replies103 threads Senior Member
    GRE:

    #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.
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