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French: 260
French and
Spanish: 140
Spanish: 140
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
81% (02:18) correct
19%
(02:41)
wrong
based on 551
sessions
History
Date
Time
Result
Not Attempted Yet
350 students at High School are currently enrolled in French, Spanish, or both French and Spanish. 230 students are currently enrolled in Spanish.
In the table, identify the number of students currently enrolled in French and the number of students currently enrolled in both French and Spanish. The two numbers must be consistent with each other and with the constraints above. Make exactly one choice in each column. (the given options are for column 3)
In the table, identify the number of students currently enrolled in French and the number of students currently enrolled in both French and Spanish. The two numbers must be consistent with each other and with the constraints above. Make exactly one choice in each column. (the given options are for column 3)
| French |
French and Spanish |
Number |
| 140 | ||
| 180 | ||
| 200 | ||
| 220 | ||
| 260 | ||
| 280 |
ShowHide Answer
Official Answer
French: 260
French and
Spanish: 140
Spanish: 140
09 Jan 2021, 06:01
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Official Explanation
Although you could draw a Venn diagram or a double-set matrix to answer this question, there is a formula for overlapping sets that will save you time:
Total = Group 1 + Group 2 + Neither – Both
In words, the total number of items equals the number of items in the first group, plus the number of items in the second group, plus the number of items in neither group, minus the number of items in both groups. (That last subtraction is necessary because the “both” items have been counted twice, as part of the first group and as part of the second group.) Apply the formula to the current problem:
Total = Spanish + French + Neither – Both
The total number of students is 350 and the number of students currently enrolled in Spanish is 230. Furthermore, all students are taking either French or Spanish or both, so the Neither category equals 0.
230 + French + 0 – Both = 350
French – Both = 120
Find 2 choices that differ by 120, with the larger number representing the total number of students currently enrolled in French and the smaller number representing the number of student enrolled in both French and Spanish. 260 and 140 are the only numbers in the list that have a difference of 120.
Column 1: The correct answer is (E).
Column 2: The correct answer is (A).
Although you could draw a Venn diagram or a double-set matrix to answer this question, there is a formula for overlapping sets that will save you time:
Total = Group 1 + Group 2 + Neither – Both
In words, the total number of items equals the number of items in the first group, plus the number of items in the second group, plus the number of items in neither group, minus the number of items in both groups. (That last subtraction is necessary because the “both” items have been counted twice, as part of the first group and as part of the second group.) Apply the formula to the current problem:
Total = Spanish + French + Neither – Both
The total number of students is 350 and the number of students currently enrolled in Spanish is 230. Furthermore, all students are taking either French or Spanish or both, so the Neither category equals 0.
230 + French + 0 – Both = 350
French – Both = 120
Find 2 choices that differ by 120, with the larger number representing the total number of students currently enrolled in French and the smaller number representing the number of student enrolled in both French and Spanish. 260 and 140 are the only numbers in the list that have a difference of 120.
Column 1: The correct answer is (E).
Column 2: The correct answer is (A).
General Discussion
17 Sep 2012, 18:14
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IMO it's 260 for french students and 140 for taking both classes.
No. taking french only = 350-230 = 120
No. of french students= 120 + No. taking both
In the numbers given only 260 = 120 + 140 can suffice the equation.
No. taking french only = 350-230 = 120
No. of french students= 120 + No. taking both
In the numbers given only 260 = 120 + 140 can suffice the equation.
