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16 Sep 2014, 01:09
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (01:48) correct
31%
(01:37)
wrong
based on 302
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If 8 apples and 10 oranges cost as much as 22 apples and 4 oranges, how much does a combination of 7 oranges and 3 apples cost?
(1) An orange costs $0.04 more than an apple
(2) The ratio of the price of an orange to the price of an apple is 7:3
(1) An orange costs $0.04 more than an apple
(2) The ratio of the price of an orange to the price of an apple is 7:3
16 Sep 2014, 01:09
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Official Solution:
If 8 apples and 10 oranges cost as much as 22 apples and 4 oranges, how much does a combination of 7 oranges and 3 apples cost?
Let \(o\) denote the price of an orange and \(a\) the price of an apple. We know from the stem that \(8a + 10o = 22a + 4o\), which gives \(14a = 6o\) and finally we get \(\frac{o}{a} = \frac{7}{3}\).
(1) An orange costs $0.04 more than an apple.
The above provides another equation: \(o = a + 0.04\). After solving the system of two linear equations for \(a\) and \(o\), we will be able to answer the question. Sufficient.
(2) The ratio of the price of an orange to the price of an apple is 7:3.
The above implies that \(\frac{o}{a} = \frac{7}{3}\). As we can see (2) just re-states the fact we already knew from the stem. So, it adds no additional useful info. Not sufficient.
Answer: A
If 8 apples and 10 oranges cost as much as 22 apples and 4 oranges, how much does a combination of 7 oranges and 3 apples cost?
Let \(o\) denote the price of an orange and \(a\) the price of an apple. We know from the stem that \(8a + 10o = 22a + 4o\), which gives \(14a = 6o\) and finally we get \(\frac{o}{a} = \frac{7}{3}\).
(1) An orange costs $0.04 more than an apple.
The above provides another equation: \(o = a + 0.04\). After solving the system of two linear equations for \(a\) and \(o\), we will be able to answer the question. Sufficient.
(2) The ratio of the price of an orange to the price of an apple is 7:3.
The above implies that \(\frac{o}{a} = \frac{7}{3}\). As we can see (2) just re-states the fact we already knew from the stem. So, it adds no additional useful info. Not sufficient.
Answer: A
09 Aug 2023, 06:22
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I think this is a high-quality question and I agree with explanation.
