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03 Aug 2026, 10:31
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At a food fair, Nora bought 8 kilograms of nuts from each of two vendors, Green Market and Riverside Market. At Green Market, almonds cost $12 per kilogram, cashews cost $14 per kilogram, and pistachios cost $17 per kilogram. At Riverside Market, the corresponding prices were $13, $15, and $18 per kilogram. Did Nora spend more money at Riverside Market than at Green Market?
(1) The ratio of almonds to cashews to pistachios that Nora bought at Green Market was \(6:1:1\).
(2) The ratio of almonds to cashews to pistachios that Nora bought at Riverside Market was \(1:3:4\).
(1) The ratio of almonds to cashews to pistachios that Nora bought at Green Market was \(6:1:1\).
(2) The ratio of almonds to cashews to pistachios that Nora bought at Riverside Market was \(1:3:4\).
03 Aug 2026, 10:31
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Official Solution:
At a food fair, Nora bought 8 kilograms of nuts from each of two vendors, Green Market and Riverside Market. At Green Market, almonds cost $12 per kilogram, cashews cost $14 per kilogram, and pistachios cost $17 per kilogram. At Riverside Market, the corresponding prices were $13, $15, and $18 per kilogram. Did Nora spend more money at Riverside Market than at Green Market?
(1) The ratio of almonds to cashews to pistachios that Nora bought at Green Market was \(6:1:1\).
The ratio at Green Market was \(6:1:1\), and Nora bought 8 kilograms there, so she bought:
6 kg almonds
1 kg cashews
1 kg pistachios
So the amount spent at Green Market was:
\(6 * 12 + 1 * 14 + 1 * 17 =\)
\(= 103\)
At Riverside Market, every listed price is at least $13 per kilogram. Since Nora bought 8 kilograms there, she must have spent more than
\(8 * 13 = 104\)
So she definitely spent more at Riverside Market than at Green Market.
Sufficient.
(2) The ratio of almonds to cashews to pistachios that Nora bought at Riverside Market was \(1:3:4\).
The ratio at Riverside Market was \(1:3:4\), and Nora bought 8 kilograms there, so she bought:
1 kg almonds
3 kg cashews
4 kg pistachios
So the amount spent at Riverside Market was:
\(1 * 13 + 3 * 15 + 4 * 18 =\)
\(= 130\)
But we do not know what mix she bought at Green Market.
For example, if she bought all 8 kilograms as almonds at Green Market, then she spent
\(8 * 12 = 96\)
So the answer would be YES.
But if she bought all 8 kilograms as pistachios at Green Market, then she spent
\(8 * 17 = 136\)
So the answer would be NO.
Not sufficient.
Answer: A
At a food fair, Nora bought 8 kilograms of nuts from each of two vendors, Green Market and Riverside Market. At Green Market, almonds cost $12 per kilogram, cashews cost $14 per kilogram, and pistachios cost $17 per kilogram. At Riverside Market, the corresponding prices were $13, $15, and $18 per kilogram. Did Nora spend more money at Riverside Market than at Green Market?
(1) The ratio of almonds to cashews to pistachios that Nora bought at Green Market was \(6:1:1\).
The ratio at Green Market was \(6:1:1\), and Nora bought 8 kilograms there, so she bought:
6 kg almonds
1 kg cashews
1 kg pistachios
So the amount spent at Green Market was:
\(6 * 12 + 1 * 14 + 1 * 17 =\)
\(= 103\)
At Riverside Market, every listed price is at least $13 per kilogram. Since Nora bought 8 kilograms there, she must have spent more than
\(8 * 13 = 104\)
So she definitely spent more at Riverside Market than at Green Market.
Sufficient.
(2) The ratio of almonds to cashews to pistachios that Nora bought at Riverside Market was \(1:3:4\).
The ratio at Riverside Market was \(1:3:4\), and Nora bought 8 kilograms there, so she bought:
1 kg almonds
3 kg cashews
4 kg pistachios
So the amount spent at Riverside Market was:
\(1 * 13 + 3 * 15 + 4 * 18 =\)
\(= 130\)
But we do not know what mix she bought at Green Market.
For example, if she bought all 8 kilograms as almonds at Green Market, then she spent
\(8 * 12 = 96\)
So the answer would be YES.
But if she bought all 8 kilograms as pistachios at Green Market, then she spent
\(8 * 17 = 136\)
So the answer would be NO.
Not sufficient.
Answer: A
