A survey was taken of children between the ages of 10 and 17 about how many siblings they have and whether they have a pet. The results of the survey are shown in the table.
| | 0 Siblings | 1 Sibling | 2 Siblings | 3 or More Siblings | Total |
| :------------ | :--------- | :-------- | :--------- | :----------------- | :---- |
| Has a Pet | 34 | 57 | | 6 | 125 |
| Does Not Have a Pet | 18 | | 15 | 2 | |
| Total | | 87 | | | 200 |
Which statement must be true?
A. Out of the 125 children who do not have a pet, 18 of them have 2 siblings.
B. Out of the 97 children who have 1 pet, 40 of them do not have any siblings.
C. Out of the 125 children who do not have any siblings, 34 of them have a pet.
D. Out of the 97 children who have 1 sibling, 40 of them do not have a pet.
Answer (2)
Calculate the missing values in the table: A = 28 (children with 2 siblings and a pet) and C = 40 (children with 1 sibling and no pet).
Evaluate each statement based on the calculated values.
Statement 1 is false because 15 children with no pet have 2 siblings, not 18.
The true statement is: Out of the 97 children who have 1 sibling, 40 of them do not have a pet. Out of the 97 children who have 1 sibling, 40 of them do not have a pet
Explanation
Analyze the problem We are given a table with information about children's siblings and pet ownership. Our goal is to determine which of the given statements must be true based on the data in the table.
Calculate missing values First, let's calculate the missing values in the table.
Let A be the number of children with 2 siblings and a pet. Let C be the number of children with 1 sibling and no pet.
From the row 'Has a Pet', we know that the total is 125. So, we have the equation: 34 + 57 + A + 6 = 125 Solving for A :
A = 125 − 34 − 57 − 6 = 28 So, there are 28 children with 2 siblings who have a pet.
From the totals, we know that the total number of children surveyed is 200. So, we have the equation: 125 + ( 18 + C + 15 + 2 ) = 200 Solving for C :
125 + 35 + C = 200 160 + C = 200 C = 200 − 160 = 40 So, there are 40 children with 1 sibling who do not have a pet.
Evaluate the statements Now, let's analyze each of the given statements:
'Out of the 125 children who do not have a pet, 18 of them have 2 siblings.' The number of children who do not have a pet is 18 + 40 + 15 + 2 = 75 . Of these 75 children, 15 have 2 siblings, not 18. So, this statement is false.
'Out of the 97 children who have 1 pet, 40 of them do not have any siblings.' This statement is incorrect. We are given that there are 34 children with 0 siblings who have a pet. The statement says 40 children with 1 pet do not have any siblings, which is false.
'Out of the 125 children who do not have any siblings, 34 of them have a pet' This statement is incorrect. There are 87 children with 0 siblings. Of these, 34 have a pet and 18 do not have a pet. The statement says 125 children do not have any siblings, which is false.
'Out of the 97 children who have 1 sibling, 40 of them do not have a pet' We calculated that there are 40 children with 1 sibling who do not have a pet. The total number of children with 1 sibling is 57 + 40 = 97 . So, this statement is true.
Final Answer Therefore, the statement that must be true is: 'Out of the 97 children who have 1 sibling, 40 of them do not have a pet'.
Examples
Understanding surveys and data analysis is crucial in many real-world scenarios. For example, a marketing company might survey potential customers to understand their preferences for a new product. By analyzing the survey data, they can determine which features are most important to customers and tailor their marketing efforts accordingly. Similarly, political campaigns use surveys to gauge public opinion and adjust their strategies to appeal to voters. In both cases, the ability to interpret and draw conclusions from survey data is essential for making informed decisions.
After calculating the missing values from the survey table, we determined that the true statement is: 'Out of the 97 children who have 1 sibling, 40 of them do not have a pet.' All other statements were found to be false based on the data provided.
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