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09 Sep 2024, 07:16
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A
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Difficulty:
95%
(hard)
Question Stats:
56% (03:01) correct
44%
(02:45)
wrong
based on 219
sessions
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Not Attempted Yet
Last year, a certain bakery’s expenses for manufacturing pretzels were equal to $70,000 plus 25% of the bakery’s total revenue from selling pretzels. If the bakery sold every pretzel it manufactured but did not make a profit on pretzel sales, did the bakery sell fewer than 18,000 pretzels last year?
(1 ) Last year, the bakery sold its pretzels for an average price of greater than $6.
(2) Last year, the bakery’s total revenue from pretzels was less than $90,000.
(1 ) Last year, the bakery sold its pretzels for an average price of greater than $6.
(2) Last year, the bakery’s total revenue from pretzels was less than $90,000.
10 Sep 2024, 11:53
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We need to determine whether the bakery sold fewer than 18,000 pretzels last year. Let:
R=70,000+0.25R => R = 70,000/(0.75) (No need to simplify this yet)
Statement (1): Last year, the bakery sold its pretzels for an average price of greater than $6.
From this, we know p>6
We know that p*N = R ( Revenue = (price of one pretzel)*(total number of pretzels) )
p*N = R => p*N = 70,000/(0.75) => p = 70,000/(0.75*N)
p>6 => 70,000/(0.75*N) > 6 => N ~< 16,000 => N < 18,000 => This is exactly what we wanted to find.
Therefore, Statement (1) is sufficient to answer the question.
Statement (2): Last year, the bakery’s total revenue from pretzels was less than $90,000.
From this, we know R<90,000but without knowing the value of p, we cannot definitively say whether N<18,000. Therefore, Statement (2) is insufficient on its own.
(A)
- N: the number of pretzels sold last year,
- R: total revenue from selling pretzels,
- C: the cost of manufacturing pretzels,
- p: the average price per pretzel.
- The bakery's expenses were 70,000+(0.25R)
- Since the bakery made no profit, its revenue R must equal its expenses C.
R=70,000+0.25R => R = 70,000/(0.75) (No need to simplify this yet)
Statement (1): Last year, the bakery sold its pretzels for an average price of greater than $6.
From this, we know p>6
We know that p*N = R ( Revenue = (price of one pretzel)*(total number of pretzels) )
p*N = R => p*N = 70,000/(0.75) => p = 70,000/(0.75*N)
p>6 => 70,000/(0.75*N) > 6 => N ~< 16,000 => N < 18,000 => This is exactly what we wanted to find.
Therefore, Statement (1) is sufficient to answer the question.
Statement (2): Last year, the bakery’s total revenue from pretzels was less than $90,000.
From this, we know R<90,000but without knowing the value of p, we cannot definitively say whether N<18,000. Therefore, Statement (2) is insufficient on its own.
(A)
28 Jan 2025, 07:49
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Quote:
not making a profit could mean breaking even or a loss. how could we be sure that revenue = cost ?
