Last year, a certain bakerys expenses for manufacturing pretzels were

Question

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.

siddhantvarma · Answer

We need to determine whether the bakery sold fewer than 18,000 pretzels last year. Let:

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.

We know that:

The bakery's expenses were 70,000+(0.25R)
Since the bakery made no profit, its revenue R must equal its expenses C.

Thus, we have the equation:

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)

livincool007 · Answer

not making a profit could mean breaking even or a loss. how could we be sure that revenue = cost ?

agrasan · Answer

Hi  GMATNinja   Bunuel   chetan2u   Bismuth83

I am a bit confused, what is wrong with my approach here?

R <= $93,300

N < 18000 ?

(1) P > $6

I started trying out different combos of P and N to check on R
Like I got  $70,000 by (7, 10000)  and  $100,000 by (10, 10000) 
We get value of R greater than $93,300 as well, hence, (1) is  insufficient

Is my approach wrong because I already assumed N<18000?

ManishaPrepMinds · Answer

Your instinct to test values is good, but the flaw is in assuming N < 18,000 to begin with , which is the very question you're asked to answer. On DS, we cannot assume what we are supposed to find out. In Statement (1), we’re told the average price per pretzel > $6 We already know: R ≤ 70,000 + 0.25R 0.75R ≤ 70,000 So, R ≤ 93,333 Now test P > 6 Try P = 7 ⇒ N = 93,333.33 ÷ 7 ≈ 13,000 P = 8 ⇒ N = 93,333.33 ÷ 8 ≈ 11000 As P increases, N decreases further So N is always < 18,000 Sufficient

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Last year, a certain bakerys expenses for manufacturing pretzels were

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