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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]

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05 May 2006, 20:52
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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.
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05 May 2006, 21:59
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.

D. nither scholarship nor loans = 30
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06 May 2006, 11:02
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.

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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07 May 2006, 04:40
I think (D) as well.

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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07 May 2006, 07:44

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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10 May 2006, 20:10
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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11 May 2006, 23:07
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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05 Aug 2006, 11:59
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.

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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05 Aug 2006, 20:51
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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05 Aug 2006, 21:42
ong wrote:
S2. n(LnS) = 30
n(not LnS)= 200 - 60 - 80 + 30 = 90
Thus, (90/200)*100 = 45%

could u explaine me more ?

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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26 Sep 2010, 12:52

Both options alone will help us find the answer so the answer is D.
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26 Sep 2010, 13:27
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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.

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.

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23 Feb 2011, 21:33
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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24 Feb 2011, 03:52
Merging similar topics.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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03 Mar 2015, 09:25
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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02 May 2016, 04:34
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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05 May 2016, 07:15
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.

Solution:

The easiest way to solve this problem is to set up a double set matrix. In our matrix we have two main categories: student loans and scholarships. More specifically, our table will be labeled with:

2) Did not receive student loans (No Loans)

4) Did not receive a scholarship (No Scholarship)

(To save room on our table headings, we will use the abbreviations for these categories)

We are given that there are a total of 200 college graduates in the survey. We also are given that 30 percent of those graduates received student loans and 40 percent received scholarships.

Thus,

200 x 0.3 = 60 received student loans

200 x 0.4 = 80 received scholarships

We are trying to determine what percent of those surveyed said that they had received neither student loans nor scholarships.

Let’s fill all this information into a table. Note that each row sums to create a row total, and each column sums to create a column total. These totals also sum to give us the grand total, designated by 200 at the bottom right of the table.

Statement One Alone:

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

Using statement one we can determine the number of students who received scholarships but no loans.

200 x 0.25 = 50 students who received scholarships but no loans.

We can fill the above information into our table.

Thus, the percent of those surveyed who said that they had received neither student loans nor scholarships is (90/200) x 100 = 45%. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

We are given that 50 percent of those surveyed who said they had received loans also said that they had received scholarships. From the given information we know that 60 students received loans; thus, we can determine the number of these 60 students who also received scholarships.

60 x 0.5 = 30 students who received loans who also received scholarships

We can fill the above information into our table.

Thus, the percent of those surveyed who said that they had received neither student loans nor scholarships is (90/200) x 100 = 45%. Statement two is sufficient to answer the question.

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Re: In a survey of 200 college graduates, 30 percent said they   [#permalink] 05 May 2016, 07:15
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