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At least 100 students at a certain high school study Japanes

This topic has 3 expert replies and 2 member replies
kaudes11114 Senior | Next Rank: 100 Posts Default Avatar
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At least 100 students at a certain high school study Japanes

Post Sun Mar 09, 2014 5:17 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?
    (1) 16 students at the school study both French and Japanese.
    (2) 10 percent of the students at the school who study Japanese also study French.

    Please help to solve

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    theCodeToGMAT Legendary Member
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    Post Sun Mar 09, 2014 7:58 am
    {B}
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    Post Sun Mar 09, 2014 8:18 am
    I'd like to point out that Rahul has done an excellent job demonstrating a technique known as the Double Matrix Method (aka Group Grid approach). 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:
    - study French or don't study French
    - study Japanese or don't study Japanese

    To learn more about the Double Matrix Method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Once you’re familiar with this technique, you can attempt these additional practice questions:

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    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

    Easy Data Sufficiency questions
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    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

    Difficult Data Sufficiency questions
    - http://www.beatthegmat.com/double-set-matrix-question-t271423.html
    - http://www.beatthegmat.com/sets-t269449.html
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

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    Post Sun Mar 09, 2014 12:15 pm
    kaudes11114 wrote:
    At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?
    (1) 16 students at the school study both French and Japanese.
    (2) 10 percent of the students at the school who study Japanese also study French.

    Please help to solve
    Alternate approach:

    Let F = the total number of students who study French, J = the total number of students who study Japanese, and B = the total number of students who study both languages.
    Since 4% of the students who study French study both languages, B = .04F.

    Statement 1: 16 students study both French and Japanese
    Thus:
    .04F = 16
    F = 400.
    No information about J.
    INSUFFICIENT.

    Statement 2: 10% of students at school who study Japanese also study French
    Thus, B = .1J.
    Since it is also true that B = .4F, we get:
    .04F = .1J
    F/J = 10/4 = 5/2.
    Thus, F>J.
    SUFFICIENT.

    The correct answer is B.

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    eitijan Master | Next Rank: 500 Posts Default Avatar
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    Post Sat May 07, 2016 4:43 am
    Hi Everyone

    I found theCodeToGMAT approach a little insufficient.
    Correct me if I am wrong
    In statement 2, we are able to find F= 250 but we dont know about exact number of J (at least 100 means 100 or greater than 100, it could be 150(less than F) or 251 (greater than F)) .
    Kindly comment.

    Post Sat Oct 14, 2017 8:16 am
    kaudes11114 wrote:
    At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?

    (1) 16 students at the school study both French and Japanese.
    (2) 10 percent of the students at the school who study Japanese also study French.
    A student asked me to provide a step-by-step solution using the Double Matrix method, so here goes....
    This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
    Here, we have a population of students, and the two characteristics are:
    - studies Japanese or does NOT study Japanese
    - studies French or does NOT study French

    Let's let J = the TOTAL number of students taking Japanese
    And let F = the TOTAL number of students taking French

    When we sketch our diagram, we get:


    Target question: Is F greater than J?

    Given: 4 percent of the students at the school who study French also study Japanese
    Since we let F = the TOTAL number of students taking French, we can say that 4% of F = number of students taking BOTH French and Japanese.
    In other words, 0.04F = number of students taking BOTH French and Japanese
    We can also say that 96% of the students who study French do NOT study Japanese
    In other words, 0.96F = number of students taking French but NOT Japanese

    So, our diagram now looks like this:


    Statement 1: 16 students at the school study both French and Japanese
    Since 0.04F = number of students taking BOTH French and Japanese, we can write: 0.04F =16
    When we solve this equation for F, we get F = 400
    So, 0.96F = 384
    So, our diagram now looks like this:


    Is this enough information to determine whether or not F is greater than J?
    No.

    For example, we COULD fill in the remaining boxes this way...

    In this case, F = 400 and J = 116, which means F IS greater than J

    However, we COULD also fill in the remaining boxes this way...

    In this case, F = 400 and J = 1016, which means F is NOT greater than J

    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: 10 percent of the students at the school who study Japanese also study French.
    J = the TOTAL number of students taking Japanese
    So, 0.1J = number of students taking BOTH French and Japanese

    Notice that we already determined that 0.04F = number of students taking BOTH French and Japanese
    So, we now have two ways to represent the SAME value.


    So, it MUST be the case that 0.1J = 0.04F
    Let's see what this tells us.
    First, to make things easier, let's multiply both sides by 100 to get: 10J = 4F
    Divide both sides by 10 to get: J = 4F/10
    Divide both sides by F to get: J/F = 4/10
    From this, we can conclude that F IS greater than J
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer: B

    Cheers,
    Brent

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