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ETS Additional Test Old Edition Question

edited Wed Sep 13, 2017 3:55 pm in Algebra
fontainedfontained Joined: 07/22/2017Posts: 23
(Admin note: The text of this question may be found in Section 5, Page 79 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)

Based on the process of elimination, I eliminated C but then I got the opposite answer to what was correct. any tricks or hints would be helpful!
Thanks

Posts

  • edited Wed Sep 13, 2017 6:55 pm
    Jonathan EvansJonathan Evans PowerScore Staff Joined: 10/31/2016Posts: 97
    Let's start with a discussion of overlapping groups, best handled by a Venn Diagram:

    We need to keep track of the following information with overlapping groups:
    1. First group by itself — "1 solo"
    2. Second group by itself — "2 solo"
    3. First group total (by itself and combined with second group) — "1 total"
    4. Second group total (by itself and combined with first group) — "2 total"
    5. Overlap between the two groups — "1&2"
    6. Total items in all groups — "Total"
    Before we discuss this question, let's look at a hypothetical example and see how the different values are related.

    Let's imagine we're taking lunch orders. 10 people order only hotdogs. 6 people order only milkshakes. 4 people order both hotdogs and milkshakes. We have 14 total hotdog orders. We have 10 total milkshake orders. There are 20 total orders.
    1. First group by itself — "H solo" = 10
    2. Second group by itself — "M solo" = 6
    3. First group total (by itself and combined with second group) — "H total" = 14
    4. Second group total (by itself and combined with first group) — "M total" = 10
    5. Overlap between the two groups — "H&M" = 4
    6. Total items in all groups — "Total" = 20
    Notice how we can combine information to calculate other values:

    "Total" = "H solo" + "H&M" + "M solo"
    20 = 10 + 4 + 6

    "H total" = "H solo" + "H&M"
    14 = 10 + 4

    "M total" = "M solo" + "H&M"
    10 = 6 + 4

    In other words, if we have partial information, we can determine other values. 

    Let's now take a look at the problem from the practice GRE:



    Let's start by setting up your scratch paper.

    It's an overlapping groups question.

    Let's see what information we know:
    1. First group by itself — "L solo"
    2. Second group by itself — "M solo"
    3. First group total (by itself and combined with second group) — "L total"
    4. Second group total (by itself and combined with first group) — "M solo" + "L&M" = "M total"
    5. Overlap between the two groups — "L&M"
    6. Total items in all groups — "Total"
    "Total" = "L solo" + "L&M" + "M solo"
    9300 = "L solo" + "L&M" + "M solo"

    "L total" = "L solo" + "L&M"
    7100 = "L solo" + "L&M"

    "M total" = "M solo" + "L&M"
    5200 = "M solo" + "L&M"

    The next step is to determine any kind of missing information we can. Look at the first two equations:

    9300 = "L solo" + "L&M" + "M solo"
    7100 = "L solo" + "L&M"

    Check out the highlighted portion of both equations. These values are present in both, so let's use simultaneous equations to get rid of them!

       9300 = "L solo" + "L&M" + "M solo"
    – 7100 = "L solo" + "L&M"
       2200 = "M solo"

    What can we figure out now? We know:

    "M total" = "M solo" + "L&M"
    5200 = "M solo" + "L&M"

    So:

    5200 = 2200 + "L&M"
    3000 = "L&M"

    Thus, we have 3000 that are distributed by both. 3000 is NOT more than half of 7100, so (A) is incorrect.

    3000 is more than half of 5200, so (B) is correct.
       
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