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24 Jan 2025, 09:28
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8-pound bags: 12,000
12-pound bags: 12,000
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.
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 Jan 2025, 09:28
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Official Solution:
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.
Correct answer:
8-pound bags "12,000"
12-pound bags "12,000"
Bunuel
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.
Correct answer:
8-pound bags "12,000"
12-pound bags "12,000"
06 Jun 2025, 03:48
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Bookmarks
Hi Bunuel,
Both of the questions has the same option as an answer. Is it applicable in the Actual GMAT test or should choose different options in TA?
Both of the questions has the same option as an answer. Is it applicable in the Actual GMAT test or should choose different options in TA?
