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16 Sep 2014, 00:23
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C
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Difficulty:
25%
(medium)
Question Stats:
72% (01:12) correct
28%
(01:22)
wrong
based on 674
sessions
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If Johnny bought candy using nickels (\($0.05\) coins) and quarters (\($0.25\) coins), how many quarters did he use?
(1) The cost of the candy Johnny bought was 85 cents.
(2) Johnny used more quarters than nickels.
(1) The cost of the candy Johnny bought was 85 cents.
(2) Johnny used more quarters than nickels.
16 Sep 2014, 00:23
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Official Solution:
If Johnny bought candy using nickels (\($0.05\) coins) and quarters (\($0.25\) coins), how many quarters did he use?
(1) The cost of the candy Johnny bought was 85 cents.
From the above, we can derive the equation \(0.05n + 0.25q = 0.85\), where \(n\) represents the number of nickels and \(q\) the number of quarters.
Multiplying the equation by 100 for simplification, we get \(5n + 25q = 85\). Further simplifying by dividing through by 5, we have: \(n + 5q = 17\).
This equation yields several integer solutions for \(n\) and \(q\):
\(n=12\) and \(q=1\);
\(n=7\) and \(q=2\);
\(n=2\) and \(q=3\);
Not sufficient.
(2) Johnny used more quarters than nickels.
This statement implies \(q > n\). On its own, this is not sufficient to answer the question.
(1)+(2) Given the condition \(q > n\) from (2), the only solution from (1) that meets this criterion is \(n = 2\) and \(q = 3\). Sufficient.
Answer: C
If Johnny bought candy using nickels (\($0.05\) coins) and quarters (\($0.25\) coins), how many quarters did he use?
(1) The cost of the candy Johnny bought was 85 cents.
From the above, we can derive the equation \(0.05n + 0.25q = 0.85\), where \(n\) represents the number of nickels and \(q\) the number of quarters.
Multiplying the equation by 100 for simplification, we get \(5n + 25q = 85\). Further simplifying by dividing through by 5, we have: \(n + 5q = 17\).
This equation yields several integer solutions for \(n\) and \(q\):
\(n=12\) and \(q=1\);
\(n=7\) and \(q=2\);
\(n=2\) and \(q=3\);
Not sufficient.
(2) Johnny used more quarters than nickels.
This statement implies \(q > n\). On its own, this is not sufficient to answer the question.
(1)+(2) Given the condition \(q > n\) from (2), the only solution from (1) that meets this criterion is \(n = 2\) and \(q = 3\). Sufficient.
Answer: C
RenanBragion
08 Jun 2020, 04:20
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I think this is a high-quality question and I agree with explanation.
