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ETS Additional Test 1st edition, Section 6, #5

edited Thu Sep 14, 2017 5:13 pm in Quant Comp
fontainedfontained Joined: 07/22/2017Posts: 23
(Admin note: The text of this question may be found in Section 6, Page 84 of the first edition of the GRE PDF practice book, archived here: https://web.archive.org/web/20110605194015/http://www.ets.org/s/gre/pdf/practice_book_GRE_pb_revised_general_test.pdf)

Usually I can get these average questions...not sure why I'm struggling on this one!

What is the best way to approach this question?

Posts

  • Jonathan EvansJonathan Evans PowerScore Staff Joined: 10/31/2016Posts: 97
    As usual, there are two approaches to this problem, a Problem Solving/Logic approach and a Textbook approach. Let's start with the Textbook Approach.

    Textbook Approach: To do this one "by the book," we need to do some quick calculations with averages. Let's take a look at how we'd set up our scratch paper. As always, Record What You Know:

    average of 100 #s = 23
    average of 50 more #s = 27

               ___A___                                    ___B___
         average of all 150 #s                         25

    Next let's do a quick average review:

    Average = Sum of All Numbers ÷ Number of Numbers

    The next step is to fill in the blanks we know here to try to figure out what we don't know:

    average of 100 #s = 23 —————> 23 = Sum of 100 Numbers ÷ 100
    average of 50 more #s = 27 ———> 27 = Sum of 50 Numbers ÷ 50

    What's the missing info here? The sums! So let's calculate those next.

    23 ∙ 100 = Sum of 100 Numbers
    27 ∙ 50 = Sum of 50 Numbers

    2300 = Sum of 100 Numbers
    1350 = Sum of 50 Numbers

    Now let's ask ourselves what we'd need to do to calculate the average of all 150. Remind yourself of the average equation:

    Average = Sum of All Numbers ÷ Number of Numbers

    Average of all 150 Numbers = Sum of all 150 Numbers ÷ 150

    Do we know the sum of all 150 numbers? Yes. It's 3650. So:

    Average of all 150 Numbers = 3650 ÷ 150 
    Average of all 150 Numbers = 24 ¹/3

    Problem Solving/Logic Approach: Notice what's going on with our averages here. We're bringing up the overall average by adding a new set of numbers. We start with 100 numbers and an average of 23. The new 50 numbers have an average of 27. 

    We wish to compare the overall average to 25.

    Key observation: What would it take to bring the overall average up to 25? Will 50 more numbers with an average of 27 be enough to bring the whole average up to 25? 

    No, it would take 100 more numbers with an average of 27 to bring the overall average up to 25.

    Think about it this way: the average of 23 and 27 is 25. If we have more 23s than 27s, we're going to be stuck closer to 23 in the overall average. 

    Therefore, without doing any calculations, you can observe that the overall average won't get up to 25, and the answer is B.

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