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 | | 97 | | | 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 total number of children who do not have a pet: 200 − 125 = 75 .
Calculate the number of children who do not have a pet and have 1 sibling: 75 − ( 18 + 15 + 2 ) = 40 .
Verify each statement against the completed table.
The true statement is: Out of the 97 children who have 1 sibling, 40 of them do not have a pet, so the answer is O u t o f t h e 97 c hi l d re n w h o ha v e 1 s ib l in g , 40 o f t h e m d o n o t ha v e a p e t .
Explanation
Analyze the problem and data We are given a table representing survey data about children's siblings and pet ownership. Our goal is to identify which statement must be true based on the information provided in the table.
Calculate missing values First, let's complete the missing values in the table.
Total children surveyed: 200
Total children who have a pet: 125
Total children who do not have a pet: 200 − 125 = 75
Total children who have 0 siblings: 34 + 18 = 52
Total children who have 1 sibling: 97
Total children who have 2 siblings: Unknown
Total children who have 3 or more siblings: 6 + 2 = 8
Now we can fill in some missing values within the table:
Children who have a pet and 2 siblings: 125 − ( 34 + 57 + 6 ) = 125 − 97 = 28
Children who do not have a pet and 1 sibling: 75 − ( 18 + 15 + 2 ) = 75 − 35 = 40
Total children who have 2 siblings: 28 + 15 = 43
Complete the table Now we have the completed table:
0 Siblings
1 Sibling
2 Siblings
3 or More Siblings
Total
Has a Pet
34
57
28
6
125
Does Not Have a Pet
18
40
15
2
75
Total
52
97
43
8
200
Evaluate each statement Now, let's evaluate each statement:
Out of the 125 children who do not have a pet, 18 of them have 2 siblings. False . Out of the 75 children who do not have a pet, 15 have 2 siblings.
Out of the 97 children who have 1 pet, 40 of them do not have any siblings. False . The statement should be 'Out of the 97 children who have 1 sibling,...'
Out of the 125 children who do not have any siblings, 34 of them have a pet. False . Out of the 52 children who have 0 siblings, 34 have a pet.
Out of the 97 children who have 1 sibling, 40 of them do not have a pet. True . This matches our completed table.
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
This type of data analysis is commonly used in market research to understand customer preferences and demographics. For example, a company might survey its customers to find out how many siblings they have and whether they own a pet. This information can then be used to tailor marketing campaigns to specific customer segments. If the company finds that customers with one sibling are more likely to buy a certain product, they can focus their marketing efforts on that group. The calculations performed in this problem, such as finding totals and differences, are fundamental to this type of analysis. Understanding these relationships helps businesses make informed decisions about their products and marketing strategies.
The accurate calculation of the survey data led to confirming that among the 97 children who have 1 sibling, 40 do not have a pet. Therefore, the correct statement is that 40 out of the 97 children with 1 sibling do not own a pet. This validation shows that the statements must be based on clear calculations and proper interpretation of the survey data.
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