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In a survey, 56 percent of the people surveyed stated [#permalink]
06 Mar 2006, 13:56

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A

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Difficulty:

45% (medium)

Question Stats:

66% (02:45) correct
34% (02:06) wrong based on 196 sessions

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?

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

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.

Re: In a survey, 56 percent of the people surveyed stated [#permalink]
25 Oct 2013, 12:42

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Re: In a survey, 56 percent of the people surveyed stated [#permalink]
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.

Re: In a survey, 56 percent of the people surveyed stated [#permalink]
16 Nov 2013, 01:10

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Expert's post

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. _________________

Re: In a survey, 56 percent of the people surveyed stated [#permalink]
08 Jan 2015, 16:15

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Re: In a survey, 56 percent of the people surveyed stated [#permalink]
08 Jan 2015, 18:23

Expert's post

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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).

Re: In a survey, 56 percent of the people surveyed stated [#permalink]
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) _________________

Re: In a survey, 56 percent of the people surveyed stated [#permalink]
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

Re: In a survey, 56 percent of the people surveyed stated [#permalink]
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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