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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 05 May 2006, 19:52
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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: DS: Survey [#permalink] New post 05 May 2006, 20:59
M8 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.


D. nither scholarship nor loans = 30
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Re: DS: Survey [#permalink] New post 06 May 2006, 10:02
M8 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.


I think it is D but am not sure as I am confused with the question.
At one point it says that 40% said they had received scholarships. Then point (1) states that 25% surveyed said they had received scholarships.
Can anyone explain this?
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 [#permalink] New post 07 May 2006, 03:40
I think (D) as well.

30% of student had loans
40% of student had scholarships

1) 25% of students said to have recieved scholarships only
Which means :
> 40 - 25 = 15 % recieved scholarships + loans
> 30 - 15 = 15 % recieved loans only

Thus : 100 - (15+25+15) = 45 % that recieved neither loans nor scholarships

>> Sufficient

2) 50% = 1/2 of students who recieved loans claimed to recieve scholarships
So :
> 30 / 2 = 15 % recieved loans & scholarships
> the other 15% got loans only
> 40 - 15 = 25 % recieved scholarships only

Thus : 100 - (15+25+15) = 45 % that recieved neither loans nor scholarships

>> Sufficient
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It is simply [#permalink] New post 07 May 2006, 06:44
The answer is D

only Scholarship : S
only Loan : L
Scholarship & Loand : B

S+L = 80 students
B+L = 60 students

from this we know that S+B+L+L = 140


To find out those received neither S nor L, we have to figure out
200 - S - B- L = 200 - (S+B+L)

all we need to know is the number of L. Also we can find out L once we know S or B.

both 1) and 2) seperately tell us one of these i.e. L or S or B

so that D is the answer.
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 [#permalink] New post 10 May 2006, 19:10
St1:
Using a venn diagram, we can work out:
(% who had both scholarships and loans) = 15%
(% who had only scholarship) = 25%
(% who had only loans) = 15%

(% who had neither) = 100 - 25 - 30 = 45%

Sufficient.

St2:
(% who had both scholarships and loans) = 15% <-- 1/2 of those who received loans also received scholarship
(% who had only scholarship) = 25%
(% who had only loans) = 15%

(% who had neither) = 100 - 25 - 30 = 45%

Sufficient.

Ans D
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 [#permalink] New post 11 May 2006, 22:07
D.
Statement 1 is sufficient: 40% said that they had received loans, 25% said that they had received only scholarships. 40-15=25 is the % of students who received both S+L. Neither S, nor L= 100-15-25-15=45
Statement 2 is sufficient: 30%*05=15, or 15% of graduates received both loans and scholarships. Hence, only loans – 15%, only scholarships – 25%, and both 15%. Neither loan, nor scholarships= 100-15-15-25=45.
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Re: PS---200 college graduates [#permalink] New post 05 Aug 2006, 10:59
ong 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


Total 200
n(L) = 0.3*200 = 60
n(S) = 0.4*200 = 80
n(not LnS)= Total - n(L)-n(S)+n(LnS)

S1. n(S-L) = 0.25*200 = 50 = n(S)-n(LnS)
n(not LnS)= 200 - 60 - 50 = 90
Thus, (90/200)*100 = 45%

S2. n(LnS) = 30
n(not LnS)= 200 - 60 - 80 + 30 = 90
Thus, (90/200)*100 = 45%

Hence, D.

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 [#permalink] New post 05 Aug 2006, 19:51
S2. n(LnS) = 30
n(not LnS)= 200 - 60 - 80 + 30 = 90
Thus, (90/200)*100 = 45%

could u explaine me more ?
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 [#permalink] New post 05 Aug 2006, 20:42
ong wrote:
S2. n(LnS) = 30
n(not LnS)= 200 - 60 - 80 + 30 = 90
Thus, (90/200)*100 = 45%

could u explaine me more ?


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

number of ppl. who received loans = 60
among those(60) 50% also received scholarships.
Thus those who received loans and scholarships = 30
Total = 200
200 = 60+80 -30 + X(those who received neither student loans nor scholarships)
X = 200 - 110 = 90.

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Re: scholarship problem [#permalink] New post 26 Sep 2010, 11:52
Based on the information given, we can deduce that 60 graduates had received a loan and 80 graduates had received a scholarship.

Both options alone will help us find the answer so the answer is D.

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Re: scholarship problem [#permalink] New post 26 Sep 2010, 12:27
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.


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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OG 67. Set [#permalink] New post 23 Feb 2011, 20:33
67. 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

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Re: OG 67. Set [#permalink] New post 24 Feb 2011, 02:52
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Re: OG 67. Set   [#permalink] 24 Feb 2011, 02:52
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