{"id":"act_quizme:math:q1:02","source_id":"act_quizme","source_item_id":"math-q1-02","external_id":"d20e63921574c9df","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":2,"scored":true,"layout_warning":null,"stem":"In the Venn diagram, circles S, C, and P represent farms raising sheep, cows, and pigs, respectively. How many of the 47 farms represented in the diagram do not raise cows? Venn diagram with circles S, C, and P. See long description for more information Long Description of Figure 1 Figure 1 The image is a Venn diagram of 3 intersecting circles. The top left circle is labeled S, 12. The top right circle is labeled C, 10. The bottom middle circle is labeled P, 5. Where only circles S and C overlap is labeled 13. Where only circles C and P overlap is labeled 4. Where only circles P and S overlap is labeled 2. Where all 3 circles overlap is labeled 1. ×","stimulus":"","stimulus_html":null,"stem_html":"

In the Venn diagram, circles S, C, and P represent farms raising sheep, cows, and pigs, respectively. How many of the 47 farms represented in the diagram do not raise cows?

\"Venn

Long Description of Figure 1
 
Figure 1
The image is a Venn diagram of 3 intersecting circles. The top left circle is labeled S, 12. The top right circle is labeled C, 10. The bottom middle circle is labeled P, 5. Where only circles S and C overlap is labeled 13. Where only circles C and P overlap is labeled 4. Where only circles P and S overlap is labeled 2. Where all 3 circles overlap is labeled 1.
×
\n
","rationale_html":"

F. Incorrect. You may have considered the number of farms that raise only pigs (12) or only sheep (5) by subtracting off the number of farms that raise both sheep and pigs, 12+5-2=15. Keep in mind that the question is asking how many farms do not raise cows, so there is no need to subtract the number of farms that might raise both sheep and pigs. 

G. Incorrect. You may have added the number of farms that raise only sheep and only pigs, 12+5=17, but forgotten to include the number of farms that raise both sheep and pigs. Keep in mind that the question asks for the number of farms that do not raise cows, which includes the number of farms that raise both sheep and pigs.

H. Incorrect. You may have thought that the 1 farm that raises all three animals should be subtracted from the total number of farms that raise only sheep, only pigs, or both sheep and pigs, 12+5+2-1=18. However, this farm is not being counted in your total of farms that raise only sheep, only pigs, or both sheep and pigs, so it does not need to be subtracted. 

J. Correct. According to the diagram, there are 12 that raise only sheep, 5 that raise only pigs, and 2 farms that raise both sheep and pigs. All the other farms raise cows. The number of farms that do not raise cows is therefore 12+5+2=19.

","correct_answer":["J"],"equiv_key":"6e3c109a10b536b056f8b5df","has_media":true,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"

15

","ord":0},{"label":"G","content_html":"

17

","ord":1},{"label":"H","content_html":"

18

","ord":2},{"label":"J","content_html":"

19

","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free on the public web; not licensed for redistribution.","redistributable":false,"item_count":78},"equivalents":[]}