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05 Mar 2024, 10:42
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Visited at least Norway: 48
Visited at least Sweden: 72
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
62% (03:35) correct
38%
(03:50)
wrong
based on 835
sessions
History
Date
Time
Result
Not Attempted Yet
In a group of 100 tourists visiting Scandinavia, 10% visited Norway, Sweden, and Denmark; 48% visited only two of these countries; 42% visited only one of these countries; and 100% visited at least one of these countries. Twenty-three tourists in the group visited at least Norway and Sweden, and 28 tourists in the group visited both Norway and Denmark. Furthermore, 3 tourists in the group visited only Denmark, and 32 tourists in the group visited only Sweden.
In the table, select the number of tourists in the group who visited at least Norway, and select the number of tourists in the group who visited at least Sweden. Make only two selections, one in each column.
In the table, select the number of tourists in the group who visited at least Norway, and select the number of tourists in the group who visited at least Sweden. Make only two selections, one in each column.
ID: 700157
| Visited at least Norway | Visited at least Sweden | |
| 40 | ||
| 48 | ||
| 54 | ||
| 62 | ||
| 68 | ||
| 72 |
ShowHide Answer
Official Answer
Visited at least Norway: 48
Visited at least Sweden: 72
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15 Mar 2024, 05:27
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This is another one of those quant set questions in the garb of a TPA question. So, as long as you have solid quant skills, you should be able to solve this question with utmost ease.
So, if you falter in this question, you should implement the stated corrective actions and once you do that not only will your ability in TPA improve but also in quant Arithmetic. 😊
Here is the video solution for you!
So, if you falter in this question, you should implement the stated corrective actions and once you do that not only will your ability in TPA improve but also in quant Arithmetic. 😊
Here is the video solution for you!
- If you were not able to translate the scenario into a Venn diagram, then the issue is your lack of conceptual understanding related to sets.
- Corrective Action: Build your conceptual understanding in sets.
- If you created the Venn diagram but were not able to fill it completely, then the issue is your translation skills when it comes to sets.
- Corrective Action: Work on process skills pertaining to sets.
- If you were not able to translate what at least Sweden or what at least Norway means, then you need to work on your translation skills.
- Corrective Action: Slow down and understand the scenario presented – at least Norway means that the student should have for sure visited Norway. They may or may not have visited any of the other two countries.
24 Mar 2024, 02:57
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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.
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.
