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26 Dec 2024, 09:00
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Line B: 16
Line C: 7
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:58) correct
27%
(02:10)
wrong
based on 666
sessions
History
Date
Time
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Not Attempted Yet
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A plant must distribute 45 hours weekly among three production lines: A, B, and C.
Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.
Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.
- Line A: Maximum 42 hours
- Line B: Maximum 20 hours
- Line C: Maximum 12 hours
Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.
Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
| Line B | Line C | |
| 6 | ||
| 7 | ||
| 8 | ||
| 16 | ||
| 17 |
ShowHide Answer
Official Answer
Line B: 16
Line C: 7
26 Dec 2024, 10:00
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Bunuel
GMAT Club's Official Explanation:
Since each line must receive more than half its maximum:
- A got at least 42/2 + 1 = 22 hours, leaving for B and C at most 45 - 22 = 23 hours.
- B must receive at least 20/2 + 1 = 11 hours.
- C must receive at least 12/2 + 1 = 7 hours.
Thus:
11 ≤ B ≤ 20
7 ≤ C ≤ 12
From the total allocation:
18 ≤ B + C ≤ 23
From the options, only B = 16 and C = 7 satisfy these conditions.
General Discussion
26 Dec 2024, 09:49
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A plant must distribute 45 hours weekly among three production lines: A, B, and C.
21 < Line A <=42
10 < Line B <=20
6 < Line C <=12
37 < Line A + Line B + Line C <=74
Line A + Line B + Line C = 45 hours
Line A is 16 or 17
Line B is 7 or 8
Case 1: Line B = 16
Line C = 7; Line A = 45-16-7 = 22; Possible
Line C = 8; Line A = 45-16-8 = 21; Not possible
Case 2: Line B = 17
Line C = 7; Line A = 45-17-7 = 21; Not Possible
Line C = 8; Line A = 45-17-8 = 20; Not possible
Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.
Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
- Line A: Maximum 42 hours
- Line B: Maximum 20 hours
- Line C: Maximum 12 hours
21 < Line A <=42
10 < Line B <=20
6 < Line C <=12
37 < Line A + Line B + Line C <=74
Line A + Line B + Line C = 45 hours
Line A is 16 or 17
Line B is 7 or 8
Case 1: Line B = 16
Line C = 7; Line A = 45-16-7 = 22; Possible
Line C = 8; Line A = 45-16-8 = 21; Not possible
Case 2: Line B = 17
Line C = 7; Line A = 45-17-7 = 21; Not Possible
Line C = 8; Line A = 45-17-8 = 20; Not possible
Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.
Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
| Line B | Line C |
| 16 | 7 |
