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In a survey, 56 percent of the people surveyed stated

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In a survey, 56 percent of the people surveyed stated [#permalink] New post 06 Mar 2006, 13:56
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In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?

A. 20%
B. 60%
C. 40%
D. 75%
E. 80%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Oct 2013, 13:28, edited 1 time in total.
Edited the question and added the OA.
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Re: PS+ Survey [#permalink] New post 06 Mar 2006, 16:32
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bewakoof wrote:
In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?

1. 20
2. 60
3. 45
4. 70
5. 80



30% of married people that not reported it = (80*3)/10
equal to 24

24+56 = 80

there you go

80 it is
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 [#permalink] New post 06 Mar 2006, 21:30
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you are right.. I thought this problem was very wordy and could not make sense of it under pressure.. thanks..
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 [#permalink] New post 09 Mar 2006, 18:12
conocieur's method is trial and error method. Substitute each Answer in the question and check if it is consistent with the information in the question.
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 [#permalink] New post 10 Mar 2006, 07:38
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let x be the % of ppl surveyed who were married.

56 + 0.3x = x

x = 80
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 25 Oct 2013, 12:42
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 16 Nov 2013, 01:04
No the solution still does not make sense to me. Let the total number of people surveyed be x.

56% stated they are married
30% stated they are not

How is the equation

56 + 0.3x = x derived here. Why are we not considering the remaining 14% people who were surveyed? I chose 80 as the answer only because it was close to 86 and luckily it is the answer here but please help me understand.
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 16 Nov 2013, 01:10
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aakrity wrote:
No the solution still does not make sense to me. Let the total number of people surveyed be x.

56% stated they are married
30% stated they are not(this is not out of the entire survey population). It is only 30% of those who are married.

How is the equation

56 + 0.3x = x derived here. Why are we not considering the remaining 14% people who were surveyed? I chose 80 as the answer only because it was close to 86 and luckily it is the answer here but please help me understand.


Let the total survey population be 100x. Now, 56x are married.

Again, let the total no of married people in the survey be 100y. Thus, 30% of them lied about being married. Thus, 70% were honest about it.

Thus, 70y = 56x

And, therefore 100y = 80x.

Thus, 80% were actually married.
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 08 Jan 2015, 16:15
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 08 Jan 2015, 18:23
Expert's post
Hi All,

This question involves "groups within groups" and you have to pay careful attention to the wording to get to the correct answer (thankfully, the math is pretty straight-forward). You can solve this problem with algebra or by TESTing VALUES.

Let's say that 100 people were surveyed.

From the first sentence, we know that there are 2 main groups of people:
1) Those who are MARRIED
2) Those who are NOT MARRIED

We're told that 56% of those who were SURVEYED stated truthfully that they were MARRIED.

56% of 100 = 56 people were married (and told the truth)

Next, we're told that 30% of those who were MARRIED did not include that information. This "30% group" is NOT 30% of 100; it's 30% of the people who were MARRIED. So in that first group (above), we have 2 sub-groups:

A) Married and told the TRUTH = 56
B) Married and did NOT tell the truth = 30% of the TOTAL 'married' group

We can now set up an equation using both these pieces of info:

X = Total married people
X = MarriedTruth + MarriedLied
X = 56 + .3(X)

Now we have 1 variable and 1 equation, so we can figure out the TOTAL number of married people...

.7X = 56
X = 80

This means that 80 TOTAL people from the original 100 surveyed are married (regardless of whether they told the truth or not).

Final Answer:
[Reveal] Spoiler:
E


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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 08 Jan 2015, 21:16
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bewakoof wrote:
In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?

A. 20%
B. 60%
C. 40%
D. 75%
E. 80%


The most important thing in sets question is to figure out the exact set that the question is talking about.

"56 percent of the people surveyed stated truthfully that they were married"

So of the 100 people 56 stated truthfully that they were married. There might have been more married people but 56 are definitely there.

"30 percent of the people surveyed who were married at that time chose not to include that information in the survey"

30% of the survey group who were married did not divulge the info. This means 70% did tell. We already know who these 70% are. They are the 56 people who said they are married.

70% of married group = 56
Married group = 56 *100/70 = 80

So 80 people out of 100 were married. Answer (E)
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 09 Feb 2015, 07:10
VeritasPrepKarishma wrote:
bewakoof wrote:
In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?

A. 20%
B. 60%
C. 40%
D. 75%
E. 80%


The most important thing in sets question is to figure out the exact set that the question is talking about.

"56 percent of the people surveyed stated truthfully that they were married"

So of the 100 people 56 stated truthfully that they were married. There might have been more married people but 56 are definitely there.

"30 percent of the people surveyed who were married at that time chose not to include that information in the survey"

30% of the survey group who were married did not divulge the info. This means 70% did tell. We already know who these 70% are. They are the 56 people who said they are married.

70% of married group = 56
Married group = 56 *100/70 = 80

So 80 people out of 100 were married. Answer (E)


My Logic is as follows. Kindly correct me if i am wrong.

Out of 100 people - 56 are married . They have confirmed.
30% didn't want to include in survey. So they are not a part of survey. --> Total number - 30

56+30 = 86 .
Remaining 14 participated in survey.

So total 70 . Out of 70, 56 are married. So 80%.

Please help.
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Re: In a survey, 56 percent of the people surveyed stated [#permalink] New post 10 Feb 2015, 21:54
Expert's post
arunrnair wrote:
VeritasPrepKarishma wrote:
bewakoof wrote:
In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?

A. 20%
B. 60%
C. 40%
D. 75%
E. 80%


The most important thing in sets question is to figure out the exact set that the question is talking about.

"56 percent of the people surveyed stated truthfully that they were married"

So of the 100 people 56 stated truthfully that they were married. There might have been more married people but 56 are definitely there.

"30 percent of the people surveyed who were married at that time chose not to include that information in the survey"

30% of the survey group who were married did not divulge the info. This means 70% did tell. We already know who these 70% are. They are the 56 people who said they are married.

70% of married group = 56
Married group = 56 *100/70 = 80

So 80 people out of 100 were married. Answer (E)


My Logic is as follows. Kindly correct me if i am wrong.

Out of 100 people - 56 are married . They have confirmed.
30% didn't want to include in survey. So they are not a part of survey. --> Total number - 30

56+30 = 86 .
Remaining 14 participated in survey.

So total 70 . Out of 70, 56 are married. So 80%.

Please help.


Focus on "% of what"...

All 100 participated in the survey, not just 70.
We are given that 30% of the set of actually married people did not tell that they are married. So 70% of the people who were married told that they are married. These 56 people constitute the 70% of the people who are married.

So 56 = 70% of Married Set
Married Set = 56*100/70 = 80
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Re: In a survey, 56 percent of the people surveyed stated   [#permalink] 10 Feb 2015, 21:54
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