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24 Dec 2024, 09:00
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8-pound bags: 12,000
12-pound bags: 12,000
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:
84% (02:18) correct
16%
(02:16)
wrong
based on 507
sessions
History
Date
Time
Result
Not Attempted Yet
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A coffee distributor must package their entire annual production of 240,000 pounds, using only a combination of 8-pound and 12-pound bags.
If they used between 10,000 and 20,000 bags of each size, select for 8-pound bags the number of 8-pound bags to be used, and select for 12-pound bags the number of 12-pound bags to be used. Make only two selections, one in each column.
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A coffee distributor must package their entire annual production of 240,000 pounds, using only a combination of 8-pound and 12-pound bags.
If they used between 10,000 and 20,000 bags of each size, select for 8-pound bags the number of 8-pound bags to be used, and select for 12-pound bags the number of 12-pound bags to be used. Make only two selections, one in each column.
| 8-pound bags | 12-pound bags | |
| 10,000 | ||
| 12,000 | ||
| 14,000 | ||
| 16,000 | ||
| 20,000 |
ShowHide Answer
Official Answer
8-pound bags: 12,000
12-pound bags: 12,000
24 Dec 2024, 10:00
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Bunuel
GMAT Club's Official Explanation:
Let x be the number of 8-pound bags and y be the number of 12-pound bags.
Equation: 8x + 12y = 240,000
Check each given option:
10,000 8-pound bags:
8(10,000) = 80,000 from 8-pound bags
Remaining = 160,000 pounds
Required 12-pound bags = 160,000 ÷ 12 = 13,333.33...
Not valid (requires non-whole number of bags)
12,000 8-pound bags:
8(12,000) = 96,000 from 8-pound bags
Remaining = 144,000 pounds
Required 12-pound bags = 144,000 ÷ 12 = 12,000
Valid solution! (12,000 is within range)
14,000 8-pound bags:
8(14,000) = 112,000 from 8-pound bags
Remaining = 128,000 pounds
Required 12-pound bags = 128,000 ÷ 12 = 10,666.67...
Not valid (requires non-whole number of bags)
16,000 8-pound bags:
8(16,000) = 128,000 from 8-pound bags
Remaining = 112,000 pounds
Required 12-pound bags = 112,000 ÷ 12 = 9,333.33...
Not valid (requires non-whole number of bags and below 10,000 minimum)
20,000 8-pound bags:
8(20,000) = 160,000 from 8-pound bags
Remaining = 80,000 pounds
Required 12-pound bags = 80,000 ÷ 12 = 6,666.67...
Not valid (requires non-whole number of bags and below 10,000 minimum)
Answer: Only the combination of 12,000 8-pound bags and 12,000 12-pound bags satisfies all requirements.
General Discussion
24 Dec 2024, 09:25
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We need to package 240,000 pounds of coffee using 8-pound and 12-pound bags. We are given that the number of bags used for each size is between 10,000 and 20,000.
Let:
x = number of 8-pound bags
y = number of 12-pound bags
The total weight equation is: 8x + 12y = 240,000
Simplify by dividing by 4: 2x + 3y = 60,000
Now, solve for different values of x:
If x = 10,000: 2(10,000) + 3y = 60,000 → 20,000 + 3y = 60,000 → 3y = 40,000 → y = 13,333.33 (not an integer)
If x = 12,000: 2(12,000) + 3y = 60,000 → 24,000 + 3y = 60,000 → 3y = 36,000 → y = 12,000 (valid solution)
If x = 14,000: 2(14,000) + 3y = 60,000 → 28,000 + 3y = 60,000 → 3y = 32,000 → y = 10,666.67 (not an integer)
If x = 16,000: 2(16,000) + 3y = 60,000 → 32,000 + 3y = 60,000 → 3y = 28,000 → y = 9,333.33 (not an integer)
If x = 20,000: 2(20,000) + 3y = 60,000 → 40,000 + 3y = 60,000 → 3y = 20,000 → y = 6,666.67 (not an integer)
Conclusion: The only valid solution is:
8-pound bags: 12,000
12-pound bags: 12,000
Let:
x = number of 8-pound bags
y = number of 12-pound bags
The total weight equation is: 8x + 12y = 240,000
Simplify by dividing by 4: 2x + 3y = 60,000
Now, solve for different values of x:
If x = 10,000: 2(10,000) + 3y = 60,000 → 20,000 + 3y = 60,000 → 3y = 40,000 → y = 13,333.33 (not an integer)
If x = 12,000: 2(12,000) + 3y = 60,000 → 24,000 + 3y = 60,000 → 3y = 36,000 → y = 12,000 (valid solution)
If x = 14,000: 2(14,000) + 3y = 60,000 → 28,000 + 3y = 60,000 → 3y = 32,000 → y = 10,666.67 (not an integer)
If x = 16,000: 2(16,000) + 3y = 60,000 → 32,000 + 3y = 60,000 → 3y = 28,000 → y = 9,333.33 (not an integer)
If x = 20,000: 2(20,000) + 3y = 60,000 → 40,000 + 3y = 60,000 → 3y = 20,000 → y = 6,666.67 (not an integer)
Conclusion: The only valid solution is:
8-pound bags: 12,000
12-pound bags: 12,000
