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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 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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In a survey of 200 college graduates, 30 percent said they [#permalink]

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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 scholarships.

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} = 0.25*200;
80 - {both} = 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]

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New post 11 Jan 2013, 04:05
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]

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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 17210 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]

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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]

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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.
(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 14540 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]

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New post 08 Oct 2014, 02:58
Quote:
(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.


Hi Bunuel,

I have been using your intersection formula and am able to solve most overlapping set questions though that. Though for this question, I don't understand the steps you used. Could you kindly provide a step by step solution for both statements. Thanks.
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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aj0809 wrote:
Quote:
(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.


Hi Bunuel,

I have been using your intersection formula and am able to solve most overlapping set questions though that. Though for this question, I don't understand the steps you used. Could you kindly provide a step by step solution for both statements. Thanks.


I re-formatted the solution to make it clearer:
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 scholarships.

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} = 0.25*200;
80 - {both} = 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.

Can you please tell me which part, if any, is still unclear? Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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New post 08 Oct 2014, 05:05
aj0809 wrote:
Quote:
(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.


Hi Bunuel,

I have been using your intersection formula and am able to solve most overlapping set questions though that. Though for this question, I don't understand the steps you used. Could you kindly provide a step by step solution for both statements. Thanks.



Dear aj0809,

You don't need solve this question fully. Consider the following equations

Let the number of people who got ONLY loan be denoted by L
Let the number of people who got ONLY scholarship be denoted by S
Let the number of people who got scholarship and loan be denoted by LS

L + LS = 30%
S + LS = 40%

1. 25 = S
We can get the value of LS and then the value of S and finally the value of those who didn't get any of these

2. LS = 15 (50% of (LS + L) = LS)
We can get the value of LS and then the value of S and finally the value of those who didn't get any of these

Thus both the equations solve our purpose.

Hence ans = D
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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New post 27 Jul 2017, 05:37
Bunuel 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?

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

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} = 0.25*200;
80 - {both} = 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.



The statement (2) confuses me, it seems like it is not exhaustive to assume the total number of those who received both.
Could it not be, that "50 percent of those surveyed who said that they had received loans also said that they had received scholarships" [... and x% of those surveyed who said that they had received scholarships also said that they had received loans.]?

Could you please correct my error in thinking and explain why the above statement cannot be a case?

Thanks in advance!
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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kodaol wrote:
Bunuel 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?

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

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} = 0.25*200;
80 - {both} = 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.



The statement (2) confuses me, it seems like it is not exhaustive to assume the total number of those who received both.
Could it not be, that "50 percent of those surveyed who said that they had received loans also said that they had received scholarships" [... and x% of those surveyed who said that they had received scholarships also said that they had received loans.]?

Could you please correct my error in thinking and explain why the above statement cannot be a case?

Thanks in advance!


Stmnt 2 does mean "50 percent of those surveyed who said that they had received loans also said that they had received scholarships" and it is exhaustive to get the total number of those who received both.

Note that when we talk about overlap of two sets, say A and B, it is enough to say that 50% of A is B too to get Both. Say A has 10 elements. 5 of those are B too. These 5 will be the only ones in A as well as B. The other 5 in A are not in B. A includes all elements that are A. So there can be no other element besides these 10 that are A. So saying that 20% of B are A too would be the same 5 elements only. Since they are A too, they MUST be in the set A. Hence, only 5 will be in Both.

Does that help?
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Re: In a survey of 200 college graduates, 30 percent said they [#permalink]

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


We can solve this question using the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of college graduates, and the two characteristics are:
- received scholarships or didn't receive scholarships
- received loans or didn't receive loans

So, we can set up our diagram as follows:
Image

In a survey of 200 college graduates...
So, we'll add the population here:
Image

...30 percent said they had received student loans
30% of 200 = 60, so 60 students received loans, which also means 140 students received no loans.
Add this to our diagram:
Image

...and 40 percent said they had received scholarships
40% of 200 = 80, so 80 students received scholarships, which also means 120 students received no scholarships.
Add this to our diagram:
Image

Target question: What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?
Let's place a star in the box that represents this portion of the population to remind us of our goal:
Image

Statement 1: 25 percent of those surveyed said that they had received scholarships but no loans
25% of 200 = 50, so 50 students can be placed in the following box:
Image

Since the boxes in the bottom row must add to 140, we can determine the value that goes in the starred box:
Image

So, 90 students received neither student loans nor scholarships.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

At this point, we'll revert back to the diagram we created with the given information:
Image

Statement 2: 50 percent of those surveyed who said that they had received loans also said that they had received scholarships.
Our diagram tells us that 60 students received loans.
50% of 60 = 30, so 30 students received loans AND scholarships
We can place this information as follows:
Image

Since the boxes in the left-hand column row must add to 80, we can determine the value that goes in the bottom-left box:
Image

Next, since the boxes in the bottom row must add to 140, we can determine the value that goes in the starred box:
Image
So, 90 students received neither student loans nor scholarships.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

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