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survey of 200 college grads

This topic has 1 expert reply and 10 member replies
gibran Senior | Next Rank: 100 Posts Default Avatar
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survey of 200 college grads

Post Tue May 20, 2008 5:43 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In a survey of 200 college graduates, 30 percent said they had received student loans during their college careers, and 40 percent said they had received scholarships. What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?
    (1) 25 percent of those surveyed said that they had received scholarships but no loans.
    (2) 50 percent of those surveyed who said that they had received loans also said that they had received scholarships.
    A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
    B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
    C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D. EACH statement ALONE is sufficient.

    OA is D. Please show the steps to resolve this problem.
    E. Statements (1) and (2) TOGETHER are NOT sufficient.

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    punit.kaur.mba Master | Next Rank: 500 Posts Default Avatar
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    Post Tue May 20, 2008 8:57 am
    Yes, Answer is (D).

    Here is the explaination -

    Notations : -

    (Total surveyed students) - T

    Students with either with Loan or Scholarship - L U S(L union S which is mathematical notation in Set Theory)

    Students with Loan and Scholarship - L Intersection S - L & S

    Students with neither - Negation(L union S) --> ~(L U S)

    Given : -

    Universal Set = Students who have either Loan or Scholarship + Students who have neither

    200 = (L U S) + ~(L U S)

    L U S = Students with Loans ( L )+ Students with Scholarships (S ) - ( L & S) [ who have both]

    Given - 30 percent said they had received student loans during their college careers

    Hence 30% of 200 = 60---> L ( Note : some of them might have scholarships)

    40 percent said they had received scholarships

    Hence 40% of 200 = 80 ---> S ( Note: some of them have Loans)

    So, L U S = 60 + 80 - (L&S)

    Stmt1:25 percent of those surveyed said that they had received scholarships but no loans

    From given S = 80
    S only( excluding people with Loans) = 25 % of 200 = 50
    Hence, People with S & L = 80 - 50 = 30

    Hence,

    L U S = 60 + 80 - 30 = 110

    ~(LUS) = T - (L U S)
    200 - 110 = 90

    Stmt1 is sufficient alone

    Stmt2 - 50 percent of those surveyed who said that they had received loans also said that they had received scholarships


    50 % of 60 = 30 ---> L & S

    Same way of solving as above,

    Stmt 2 is Sufficient

    Hence Answer is (D)

    chidcguy Master | Next Rank: 500 Posts Default Avatar
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    Post Tue May 20, 2008 4:58 pm
    Don't you think the MGMAT way of solving the problem is easier with the grid?

    Thanks for a fresh perspective though.

    punit.kaur.mba Master | Next Rank: 500 Posts Default Avatar
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    Post Tue May 20, 2008 6:16 pm
    I agree solving the problem the way I did would be a little time consuming . But somehow, I am confident of the answer when I do it my usual way.

    I haven't gone through any of Quant material or strategies yet. If I come across anything good which will save me time, I'll definitely go for tht.

    Which Mgmat method r u talking about? What is the book u r using for quant?

    akshatsingh Senior | Next Rank: 100 Posts Default Avatar
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    Post Tue May 20, 2008 9:21 pm
    I solved it by venn diagram.
    It was really easy with that.

    Try it to be quick.

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    varunkh70 Senior | Next Rank: 100 Posts Default Avatar
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    Post Fri Jul 31, 2009 6:16 pm
    This can certainly be solved by Venn Diagrams but a faster method would be to use the charting method suggested by Manhattan. But, I have a doubt with charting here Confused Can Ne1 suggest where am I goin wrong? Here is the chart.

    S=>NO. OF STUDENTS WHO RECEIVED SCHOLARSHIPS.
    NS=>NO. OF STUDENTS WHO DID NOT RECEIVE SCHOLARSHIPS.
    L=>NO. OF STUDENTS WHO RECEIVED LOANS
    NL=>NO. OF STUDENTS WHO DID NOT RECEIVE LOANS
    T=>TOTAL

    30% = 60

    40% = 80

    -----S -------NS-----T

    L-------------------- 60(GIVEN)


    NL------------?------140


    T----80------120----200
    (GIVEN)

    Stmt 1 =>

    25% = 50

    -----S -------NS--------T

    L----30-----------------60(GIVEN)


    NL---50------90--------140


    T----80-------120------ 200
    (GIVEN)

    sufficient since this gives me the answer (but watch the no. of students with both loans and scholarships =30 get conflicted by stmt 2)

    Stmt 2 = > students with S&L 50% = 100 (which opposes stmt1). Why is this so? Its firmly believed that two stmts cant oppose each other.

    Additionally, the total comes to 80 then how can s&l be 100? I think I am making a mistake somewhere.Can ne plz help?

    cubicle_bound_misfit Master | Next Rank: 500 Posts
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    Post Sat Aug 01, 2009 5:43 am
    varunkh,

    This is how I see it.


    S scholarship L loan T total
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    Stacey Koprince GMAT Instructor
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    Post Fri Aug 07, 2009 8:39 am
    Received a PM asking me to respond, specifically in terms of how to use the Double-Set Matrix (the MGMAT grid method) to solve the problem.

    It's a little tough graphically to show the grid here, so bear with me if the formatting looks funny.

    First set: loan vs. no loan
    Second set: scholarship vs. no scholarship

    Find: no loan and no scholarship

    .............S.........NS.........Tot
    L
    NL.....................??
    Tot...............................200

    30% = L. 30% of 200 = 60.

    .............S.........NS.........Tot
    L...................................60
    NL.....................??........200-60
    Tot...............................200

    40% = S. 40% of 200 = 80

    .............S.........NS.........Tot
    L...................................60
    NL.....................??.........140
    Tot........80.......200-80.....200

    Statement 1:
    25% of total = S and NL
    25% of 200 = 50

    .............S.........NS.........Tot
    L...................................60
    NL.........50..........??........140
    Tot........80..........120......200

    Can solve for NL + NS. Sufficient.

    Statement 2:

    50% of L's also had S's. [Note: NOT 50% of the total 200! Go read the sentence again. The word "who" is the key - it changes the meaning and tells you we're taking a percentage of a subset, not the overall group!]
    L's = 60, so 50% of 60 = 30.

    .............S.........NS.........Tot
    L...........30......................60
    NL.....................??.........140
    Tot........80.......200-80.....200

    Can solve for NL + NS. Sufficient.

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    malman Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sun Jul 10, 2011 9:44 am
    Thanks for explaining that Stacey. I'm just not sure about one part. The question says 50% of students who received loans also got scholarships. Is this the total number of students who received both loans and scholarships? Wouldn't they also need to have the percentage of scholarship receiving students who also received loans?

    ikaplan Master | Next Rank: 500 Posts
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    Post Sun Jul 10, 2011 11:13 am
    For these kind of problems, I always use the grid- the results are evident- thanks to the grid, 99% of my answers are correct.

    I find the grid equally useful both for PS and DS questions. Once you master it, the grid is in your blood Wink

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    navami Legendary Member
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    Post Tue Jul 12, 2011 9:08 am
    Venn dia gram . both sufficient

    Scholarship = 50 students
    Scholarship + Loan = 30

    Loan alone = 30 students

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    vijaykondepudi Newbie | Next Rank: 10 Posts Default Avatar
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    Post Thu Jan 03, 2013 4:54 am
    I see there is a question in this thread from malman, which is not answered:

    Quote:
    Thanks for explaining that Stacey. I'm just not sure about one part. The question says 50% of students who received loans also got scholarships. Is this the total number of students who received both loans and scholarships? Wouldn't they also need to have the percentage of scholarship receiving students who also received loans?
    I had a similar doubt regarding Statement II.

    Statement 2 says:

    (2) 50 percent of those surveyed who said that they had received loans also said that they had received scholarships.

    50 % of those that received scholarships also received loans. If I assume that the overlap set consists of
    Case 1> People from those who received Scholarships who also received Loans
    +
    Case 2> People from those who received Loans, who also received Schorlarships

    Statement II, addresses only the Case 1, with no information about case 2.

    How can we say it's sufficient ?

    Thank You !!

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