In a survey, 56 percent of the people surveyed stated

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)
_________________

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.
_________________

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

24+56 = 80

there you go

80 it is

you are right.. I thought this problem was very wordy and could not make sense of it under pressure.. thanks..

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.

let x be the % of ppl surveyed who were married.

56 + 0.3x = x

x = 80

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.

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:

GMAT assassins aren't born, they're made,
Rich

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
_________________

One can use grid method to always solve problems such as these.
Yes...it will take a little longer time but will be 100% accurate if done correctly.
Check the attachment for the solution.

As always I have a different approach ( God knows When I can start thinking things straight and simple )

Let total no of people surveyed be 1000
Total no of people surveyed stated truthfully that they were married is 560

30% didnt state truthfully about their marriage

So, 70% stated truthfully about their marriage.



From the above data we know 70% = 560
So, 1% = 560/70%

Total no of married people in the survey is (560/70)*100 = 800

Total no of people surveyed is 1000 and out of them 800 people were married , so percentage of people who were married is 80%

Answer is (E) 80%

_________________

suppose total % of people who were married is x.
now, 56% mentioned that they were married, while 30% of those who were married did not mention that.
it means that 56% is actually 70% of x.
so 56=7x/10
x=56*10/7
x=80.

We can let the total number of people surveyed = 100 and the number of people who were actually married = n. So, 56 people stated truthfully that they were married and 0.3n people who were married chose not to state that they were married. Thus:

56 + 0.3n = n

56 = 0.7n

n = 56/0.7 = 560/7 = 80

Since 80 people were actually married and there were 100 people in the survey, the percentage of the people surveyed who were actually married is 80%.

Alternate Solution:

Since 30% of the married population did not include the information about their marital status, 70% of the married population did include this information, and they correspond to 56% of the total number of people surveyed. We can set up a direct proportion to determine the actual percentage of the married people: Let x denote the percentage of the married people among the people who were surveyed:

70/56 = 100/x

70x = 5600

x = 80

Answer: E
_________________

Let us consider that total people = 100
Married (Declared) = 56
Actual Married = 56 + x
Now of these actual married 30% lied.
So,
x = 0.3(56 + x)
0.7x = 0.3 * 56
x = 0.3 / 0.7 * 56
x = 24

So in total Actual Married = 56 + 24 => 80

So here we have only two kinds of People, people who revealed that they are married and who did not reveal. No third kind of people who revealed but lied that they are married.