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Thread: Need Help with a Difficult Combinations Question

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    Need Help with a Difficult Combinations Question

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    Hello, everyone! So I came across this rather difficult practice combinations question on magoosh.com, and while the answer was given, the explanation for it was not. Here is the question (and the answer hidden by a spoiler tag):

    An artist is planning on mixing together any number of different colors from her palette. A mixture results as long as the artist combines at least two colors. If the number of possible mixtures is less than 500, what is the greatest number of colors the artist could have in her palette? (A) 8 (B) 9 (C) 11 (D) 12 (E) 13

    Would anyone happen to know exactly how to approach this question?


    SPOILER: The answer to the question was A (8.)


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    Re: Need Help with a Difficult Combinations Question

    Quote Originally Posted by Topher66 View Post
    Hello, everyone! So I came across this rather difficult practice combinations question on magoosh.com, and while the answer was given, the explanation for it was not. Here is the question (and the answer hidden by a spoiler tag):

    An artist is planning on mixing together any number of different colors from her palette. A mixture results as long as the artist combines at least two colors. If the number of possible mixtures is less than 500, what is the greatest number of colors the artist could have in her palette? (A) 8 (B) 9 (C) 11 (D) 12 (E) 13

    Would anyone happen to know exactly how to approach this question?


    SPOILER: The answer to the question was A (8.)

    Let there be n colors in her palette.
    The no. of ways to make a mixture of 2 or more colors is nC2 + nC3 ... nCn <= 500.
    Now, add nC0 + nC1 = n+1 to both sides. This gives 2^n <500+n+1. Now just find the smallest integer n which solves this problem. Answer comes to (A) 8.

    To check, see that 2^9 does not satisfy the inequality.

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    Re: Need Help with a Difficult Combinations Question

    Thank you so much for this! It is certainly helpful to finally have an explanation for this question!

    Best wishes,
    —Topher

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    Re: Need Help with a Difficult Combinations Question

    Thank you so much for this! It is certainly helpful to finally have an explanation for this question!

    Best wishes,
    —Topher

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    Re: Need Help with a Difficult Combinations Question

    Hello Topher,

    I recently took GRE and have scored really bad in Maths and English both. My practice test (Manhattan series scores were somewhere between 313 and 316 ) but I got 305 in main exam.

    I am thinking to prepare again for exam and retake it. Any idea/inputs on how to improve on the following
    1) Statistics
    2) Inequality
    3) Permutation and combination
    4) Probabilyt

    I have somehow felt that in second section of Maths some of the questions were quiet tough than I have seen earlier in any of the exam I took. Can you please let me know if you have any suggestions?

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    Re: Need Help with a Difficult Combinations Question

    Hello, again, Shreya! So, the first thing I have to suggest if you're struggling is to check out the website magoosh.com—this is the website for a company that is specifically dedicated to helping students prepare for the GRE. They have practice questions, most of which have explanations to them (with certain exceptions such as the one you see here), for all of those concepts which you listed as areas in which you struggle. They are definitely a good first place to start. If you want even a little bit more preparation than this, then I would definitely suggest looking up some online websites that help in teaching math—for instance, there's a YouTube series titled something along the lines of "Paul's Online Math Notes" that might be of some help. For the verbal reasoning (English) portion, I would suggest just putting in a google search of "GRE Vocabulary Words" and making flashcards for about five words each day—knowing the words that appear on the test is the main part of mastering the verbal reasoning portion.

    A couple of quick and important notes as well before I submit this reply: when I was taking the actual exam myself (which I have finally completed), I felt at a couple of times as if I was doing very poorly and would have to retake the exam, but I got a 163 on the verbal reasoning test and a 162 on the quantitative reasoning test. So, keep in mind that while you may feel like you are doing very poorly on a test, you could very easily be doing much better than you realize. You may also do more poorly on practice tests than you do on the actual exam—I know I sure did. So definitely never let a practice test dishearten you—they're often much more difficult than the actual test itself.

    Finally, be wary of practice test that still use the 700-point scale. The most recent edition of the GRE has scores ranging from 130-170. If you receive a score like "305" or so on a particular practice test, be warned that whichever practice test you are taking may be a bit outdated.

    I hope this is helpful for you. Best of luck on the exam!

    Sincerely,
    —Topher

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