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In a survey of 200 college graduates, 30 percent said they

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In a survey of 200 college graduates, 30 percent said they [#permalink] New post 26 Sep 2010, 10:47
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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.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink] New post 08 Feb 2012, 04:40
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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?

30 percent received student loans --> 200*0.3=60 graduates received loans;
40 percent received scholarships --> 200*0.4=80 graduates received loans;

200={loans}+{scholarships} - {both}+{neither} --> 200=60+80-{both}+{neither} --> {neither}=60+{both}. Question: {neither}=?

As {neither}=60+{both} then we should calculate # of students who received both loans and scholarships.

(1) 25 percent of those surveyed said that they had received scholarships but no loans --> {scholarships} - {both}=80 - {both}=0.25*200=50 --> {both}=80-50=30 --> {neither}=60+{both}=60+30=90. Sufficient.

(2) 50 percent of those surveyed who said that they had received loans also said that they had received scholarships --> 0.5*{loans}={both} --> 0.5*60=30={both} --> {neither}=60+{both}=60+30=90. Sufficient.

Answer: D.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink] New post 11 Jan 2013, 03:05
Is it possible to have a table approach for this question, I find it easier to answer these type of questions. Any help will be appreciated. Thanks!

my question is regarding statement 2 the way to comprehend this question is that 50 percent of those who had taken loans? it isn't 50 percent of those who had surveyed right.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink] New post 11 Jan 2013, 08:59
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Based on the information given in the question stem we can put below information in the statistics table.

Attachment:
Students.jpg
Students.jpg [ 99.12 KiB | Viewed 3735 times ]


We need to find "neither" i.e. "students with neither loans nor scholarships" - Marked in RED.
So if DS statement gives any information about the cells in YELLOW will lead you to calculated answer.

Statement(1)
SUFFICIENT: 25% (i.e. 50 students) are with scholarships but no loans. Based on this arrive at the answer "neither" = 90 (check the above image)

Statement(2)
SUFFICIENT: 50% of students with loans -> received scholarship i.e. 50% of 60 = 30 students. Based on this arrive at the answer "neither" = 90.

Hence choice(D) is the answer.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink] New post 11 Jan 2013, 09:05
fozzzy wrote:
Is it possible to have a table approach for this question, I find it easier to answer these type of questions. Any help will be appreciated. Thanks!

my question is regarding statement 2 the way to comprehend this question is that 50 percent of those who had taken loans? it isn't 50 percent of those who had surveyed right.


my question is regarding statement 2 the way to comprehend this question is that 50 percent of those who had taken loans? it isn't 50 percent of those who had surveyed right.
-- "who said that they had received loans" is acting as a modifier for "those surveyed" and thus restricts its scope to students with loans. That means, 50% of students with loans -> also received scholarships.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink] New post 24 Apr 2014, 03:56
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink] New post 24 Apr 2014, 21:53
Expert's post
udaymathapati wrote:
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.



In my opinion, Venn diagrams are most effective in solving such questions.

Students who received loans = 30% of 200 = 60
Students who received schol = 40% of 200 = 80

Attachment:
Ques3.jpg
Ques3.jpg [ 13.55 KiB | Viewed 1078 times ]

There are 3 regions in the figure - red identifying people who received only loans. Yellow for people who received only scholarships and orange for those who received both. To get neither, i.e. the white region, we need to know how many receive both - the orange region.

200 - Neither = 60 + 80 - Both

(1) 25 percent of those surveyed said that they had received scholarships but no loans.
This tells us that the yellow region is 50. This means the orange region is 30 since the entire circle is 80. This gives us both and hence is enough to answer the question.

(2) 50 percent of those surveyed who said that they had received loans also said that they had received scholarships.
50% of people who received loans received scholarships too. Since 60 people received loans, 30 received scholarships too. This means orange region is 30 i.e. both is 30. This statement alone is also sufficient to answer the question.

Answer (D)
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Re: In a survey of 200 college graduates, 30 percent said they   [#permalink] 24 Apr 2014, 21:53
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