In a group of 100 tourists visiting Scandinavia, 10% visited Norway

Given,
Visited all three countries= 10
Visited only 2 countries=48
Assuming,
>> Visited both norway and sweden only = x
>> Visited both denmark and sweden only = y
>> Visited both norway and denmark only =z
x+y+z= 48----1

>> Norway only = a
>> Sweden only = b
>> Denmark only = c

a+b+c=42-----2
Now,

Given that : a =3 & c=32>> b=7(from eq2)

Given that:
Twenty-three tourists in the group visited at least Norway and Sweden
>>x+10=23 --> x=13
28 tourists in the group visited both Norway and Denmark
>> y+10=28 --> y=18
From eq 1 z= 17

Ques asks
1. Atleast Norway: a+x+y+10 = 7+13+18+10= 48
2. Atleast Sweden : b+x+z+10= 32+13+17+10=72

All this can be done through venn diagram as well.

chetan2u any other way to solve it?

it's taking forever to solve the venn diagram, any way I can do it faster, or should I just work on speeding the process up?

Official answer:
Consider the Venn diagram above with labels N, S, and D for Norway, Sweden, and Denmark, respectively, and variables a through g representing numbers of the 100 tourists visiting these countries.


Since 10% of the tourists visited Norway, Sweden, and Denmark, it follows that g = 0.10(100) = 10.

Also, 28 tourists in the group visited both Norway and Denmark, so d + g = d + 10 = 28, from which d = 18.

Furthermore, 23 tourists in the group visited at least Norway and Sweden, so e + g = e + 10 = 23, from which e = 13.

Since 32 tourists in the group visited only Sweden, b = 32.

It is given that 48% of the tourists or 0.48(100) = 48 visited only two of the countries, from which it follows that d + e + f = 48, so 18 + 13 + f = 48 from which f = 17.

Given that 3 tourists in the group visited only Denmark, c = 3.



The number of the 100 tourists who visited at least Norway is 7 + 13 + 10 + 18 = 48.

The correct answer is 48.


The number of the 100 tourists who visited at least Sweden is 13 + 32 + 17 + 10 = 72.

The correct answer is 72.

Given that 42% of the 100 tourists visited only one of these countries, a + b + c = 0.42(100) = 42, from which it follows that a + 32 + 3 = 42 and a = 7.

The Venn diagram below shows the values of a through g.­

Took me 4.30 mins to solve the question after seeing the solution. How on earth can anyone solve it under 3 mins on the first attempt with such difficult wording?

Really annoys me how some of these OG questions have clear flaws in them.

They should have indicated whether the 28 tourists that visited Norway and Denmark ONLY visited those two countries or if they AT LEAST visited those two questions.

If I got a question with such a discrepancy on the actual exam, I would be very frustrated because you basically have to solve it twice.

There is no discrepancy.
When it says 28 people visited both N and D, it means all those who visited just these two plus all this who visited all three countries.

If they mean just the two, then they would add words such as ‘only’ or ‘exactly’ or something similar to it.

Posted from my mobile device

There very clearly is a discrepancy, I’m not sure that part is up for debate lol.

They literally use “at least” and “both” interchangeably; however, how is a student supposed to infer that they are using them interchangeably?

Other than someone with prior knowledge, a student has no way of knowing. They use “at least” in every other instance in the question stem when they refer to that group plus some, and use “only” in all the other instances where they refer to only those groups specifically.

The use the term “both” only once and I’m fairly confident they didn’t intend on making the question more dependent on understand the meaning of “both” than anything conceptual.

Completely agree with you. Seems like the english quality of gmat is getting poorer and poorer. At least clearly, means at a minimum and not exactly.
­

Totally agree! As I just checked, the word "both" referred : used for emphasis to refer TWO people or things, regarded and identified together

Completely agree with wolfof6thstreet - 100% - In this batch of questions I think GMAC really dropped the ball.

I mean look at this poorly written sentence: "Twenty-three tourists in the group visited at least Norway and Sweden, and 28 tourists in the group visited both Norway and Denmark"

1) There's inconsistency between spelling out numbers and using digits, like 'Twenty-three' vs '28.'
2) The first part of the sentence uses 'at least,' but it's dropped in the second half, making it unclear whether the second figure is exact or also 'at least.'

So now, I'm not sure if it's exact or if its at least again. Is this on purpose. Would an extra "at least" have taken up so much space. Why can't they a bit more clear with their writing and language?

Hi chetan2u
There really seems to be a discrepancy. They are using different words but treating it the same way while solving. Please check and clarify..Its really unhealthy for us to have this unsorted.