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31 May 2026, 08:31
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Total workers: 34
Workers in all three: 4
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
63% (02:50) correct
37%
(03:01)
wrong
based on 750
sessions
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Time
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The workers in an office are placed into three working groups, each containing 20 workers. All workers are in at least one group. Any 2 groups have exactly 10 members in common.
Identify in the table two numbers that are jointly consistent with the given information: the total number of workers in the office, and the number of workers who are members of all three groups. Make only two selections, one in each column.
Identify in the table two numbers that are jointly consistent with the given information: the total number of workers in the office, and the number of workers who are members of all three groups. Make only two selections, one in each column.
| Total workers | Workers in all three | Number |
| 4 | ||
| 8 | ||
| 10 | ||
| 18 | ||
| 34 | ||
| 45 |
ShowHide Answer
Official Answer
Total workers: 34
Workers in all three: 4
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02 Jun 2026, 03:34
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The workers in an office are placed into three working groups, each containing 20 workers. All workers are in at least one group. Any 2 groups have exactly 10 members in common.
Identify in the table two numbers that are jointly consistent with the given information: the total number of workers in the office, and the number of workers who are members of all three groups. Make only two selections, one in each column.
For this one, we can use the following formula for three overlapping sets.
Total = A + B + C - (The Double Overlaps) + (The Triple Overlap)
So, we have the following:
Total = 20 + 20 + 20 - (10 + 10 + 10) + (The Triple Overlap)
Total = 30 + (The Triple Overlap)
Scanning the choices, we see that only two are 30 apart, 34 and 4.
Correct answer: 34, 4
Identify in the table two numbers that are jointly consistent with the given information: the total number of workers in the office, and the number of workers who are members of all three groups. Make only two selections, one in each column.
For this one, we can use the following formula for three overlapping sets.
Total = A + B + C - (The Double Overlaps) + (The Triple Overlap)
So, we have the following:
Total = 20 + 20 + 20 - (10 + 10 + 10) + (The Triple Overlap)
Total = 30 + (The Triple Overlap)
Scanning the choices, we see that only two are 30 apart, 34 and 4.
Correct answer: 34, 4
General Discussion
31 May 2026, 08:38
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Official Explanation :
Infer:
For any three sets, |A| + |B| + |C| - (|A intersection B| + |A intersection C| + |B intersection C|) + |A intersection B intersection C| = |A union B union C|.
The left side of the equation becomes 20 + 20 + 20 - (10 + 10 + 10) + |A intersection B intersection C|, which is 30 + |A intersection B intersection C|.
This establishes the desired relationship (the total number of workers is 30 greater than the number of workers in all three).
Total workers: The correct answer is 34.
Workers in all three: The correct answer is 4.
Infer:
For any three sets, |A| + |B| + |C| - (|A intersection B| + |A intersection C| + |B intersection C|) + |A intersection B intersection C| = |A union B union C|.
The left side of the equation becomes 20 + 20 + 20 - (10 + 10 + 10) + |A intersection B intersection C|, which is 30 + |A intersection B intersection C|.
This establishes the desired relationship (the total number of workers is 30 greater than the number of workers in all three).
Total workers: The correct answer is 34.
Workers in all three: The correct answer is 4.
