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16 Sep 2014, 00:57
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If 4 small boxes and 5 big boxes have the same weight as 11 small boxes and 2 big boxes, how much does a single small box weigh?
(1) A big box weighs 1 kg more than a small box.
(2) The weight ratio of a small box to a big box is \(\frac{3}{7}\).
(1) A big box weighs 1 kg more than a small box.
(2) The weight ratio of a small box to a big box is \(\frac{3}{7}\).
16 Sep 2014, 00:57
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Official Solution:
If 4 small boxes and 5 big boxes have the same weight as 11 small boxes and 2 big boxes, how much does a single small box weigh?
From the information provided: \(4s + 5b = 11s + 2b\), which simplifies to \(3b = 7s\). Our goal is to determine the value of \(s\).
(1) A big box weighs 1 kg more than a small box.
The above implies that \(b = s + 1\). Substituting for \(b\) in our equation, we get \(3(s + 1) = 7s\), which yields \(s = \frac{3}{4}\). Sufficient.
(2) The weight ratio of a small box to a big box is \(\frac{3}{7}\).
This gives \(\frac{s}{b} = \frac{3}{7}\), which leads to \(3b = 7s\), the same relationship we derived from the initial statement. Hence, this doesn't give additional information to determine the weight of a small box by itself. Not sufficient.
Answer: A
If 4 small boxes and 5 big boxes have the same weight as 11 small boxes and 2 big boxes, how much does a single small box weigh?
From the information provided: \(4s + 5b = 11s + 2b\), which simplifies to \(3b = 7s\). Our goal is to determine the value of \(s\).
(1) A big box weighs 1 kg more than a small box.
The above implies that \(b = s + 1\). Substituting for \(b\) in our equation, we get \(3(s + 1) = 7s\), which yields \(s = \frac{3}{4}\). Sufficient.
(2) The weight ratio of a small box to a big box is \(\frac{3}{7}\).
This gives \(\frac{s}{b} = \frac{3}{7}\), which leads to \(3b = 7s\), the same relationship we derived from the initial statement. Hence, this doesn't give additional information to determine the weight of a small box by itself. Not sufficient.
Answer: A
23 Oct 2023, 00:56
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
