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In a survey of 200 college graduates, 30 percent said that they had re
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07 Nov 2023, 10:43
07 Nov 2023, 10:43
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In a survey of 200 college graduates, 30 percent said that they had received student loans during their college careers, and 40 percent said that they had received scholarships. If 25 percent of those surveyed said that they had received scholarships but no loans, what percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?
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Re: In a survey of 200 college graduates, 30 percent said that they had re
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14 Nov 2023, 17:44
14 Nov 2023, 17:44
1
Let us try to solve using Venn-diagrams:
Given , Student loans (SL) = 30% and Scholarships (SS) = 40% , and Only Scholarships , but no loan (Only SS) = 25%
So the student loans data comprises of students who received only student loans and who received both student loans and scholarships
Similarly the scholarship data comprises of students who received only scholarships and who received both scholarships and student loans
Thus Total = Only SL + Only SS + Both + Neither -- (Eqn1)
Now SS = Only SS + Both --> 40% = 25% + Both --> Both = 40% - 25% = 15%
and SL = Only SL + Both --> 30% = Only SL + 15% --> Only SL = 15%
Thus if we consider the total to be 100% then we can write the Eqn 1 as --> 100 = 15 + 25 + 15 + Neither
Thus, Neither = 100 - 55 = 45%
Given , Student loans (SL) = 30% and Scholarships (SS) = 40% , and Only Scholarships , but no loan (Only SS) = 25%
So the student loans data comprises of students who received only student loans and who received both student loans and scholarships
Similarly the scholarship data comprises of students who received only scholarships and who received both scholarships and student loans
Thus Total = Only SL + Only SS + Both + Neither -- (Eqn1)
Now SS = Only SS + Both --> 40% = 25% + Both --> Both = 40% - 25% = 15%
and SL = Only SL + Both --> 30% = Only SL + 15% --> Only SL = 15%
Thus if we consider the total to be 100% then we can write the Eqn 1 as --> 100 = 15 + 25 + 15 + Neither
Thus, Neither = 100 - 55 = 45%
gmatclubot
Re: In a survey of 200 college graduates, 30 percent said that they had re [#permalink]
14 Nov 2023, 17:44
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