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Thread: please show the best way to solve this problem

  1. #1
    Trying to make mom and pop proud
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    please show the best way to solve this problem

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    What is the best way to solve problems like this:

    If 75% of a class answered the first question on a certain test correctly, 55% answered the second question on the test correctly, and 20% answered neither of the questions correctly, what percent answered both correctly?

    Please advise. . .

    Thanks

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    Trying to make mom and pop proud
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    Any help please?

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    An Urch Guru Pundit Swami Sage
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    I just brake it up on the first question. 75% answered it write, 20% got it wrong and question 2 wrong, so 5% must have answered it wrong, but gotten question 2. That means that 50 of the 55% that got question two must have gotten question one as well. So 50% is your answer.

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    Spasibo!

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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    We can solve this question using the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
    Here, we have a population of students, and the two characteristics are:
    - answering question #1 correctly or incorrectly
    - answering question #2 correctly or incorrectly
    Since the question asks us to find a PERCENT, let's say we have 100 students in TOTAL
    So, we can set up our Matrix as follows:

    As we can see, 50 of the 100 students correctly answered BOTH questions.

    To learn more about this technique, watch our free video: http://www.youtube.com/watch?v=jK-tiBrrf04

    Cheers,
    Brent - GMAT Prep Now
    Attached Thumbnails Attached Thumbnails please show the best way to solve this problem-test.png  

  6. #6
    Trying to make mom and pop proud
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    Just.. pen down the Ven Diagram

    (75-x) + (55-x) + x +20 = 100
    Solve for x, x =50%. Note x = Intersection Area

  7. #7
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    100-20=80............Now (75+55)-80 =50

  8. #8
    GMAT and LSAT Tutor
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    I tend to use the method to map it out. The first thing you fill out is the total for Q1 right, which we know is 75, then you can fill out the total for Q2 right which is 55.
    You also can fill out the Q1 wrong and Q2 wrong as 20 and the total total is 100, so it will look like this:

    Q1 right Q1 wrong Total
    Q2 right 55
    Q2 wrong 20
    Total 75 100

    From there, you can figure out the total for Q2 wrong and Q1 wrong by subtracting the percentage right from the total

    Q1 right Q1 wrong Total
    Q2 right 55
    Q2 wrong 20 45
    Total 75 25 100


    Then you can use the 20 wrong to figure out the rest by subtracting it from the totals and so forth

    Q1 right Q1 wrong Total
    Q2 right 50 5 55
    Q2 wrong 25 20 45
    Total 75 25 100


    so you know that 50% of people answered both correctly

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