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# On a certain day, a bakery produced a batch of rolls at a total produc

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Joined: 01 Sep 2010
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On a certain day, a bakery produced a batch of rolls at a total produc [#permalink]

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25 Jul 2017, 11:43
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Difficulty:

55% (hard)

Question Stats:

70% (02:27) correct 30% (02:24) wrong based on 379 sessions

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On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, $$\frac{4}{5}$$ of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls? A.$ 150

B. $144 C.$ 132

D. $108 E.$ 90

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On a certain day, a bakery produced a batch of rolls at a total produc [#permalink]

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25 Jul 2017, 14:16
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carcass wrote:
On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, $$\frac{4}{5}$$ of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls? A.$ 150

B. $144 C.$ 132

D. $108 E.$ 90

Method I - assign a value to number of rolls total

Because all the rolls are sold, and because they are all sold at equal prices on their respective days, we can use any number of rolls we want to calculate profit as Total revenue - Total cost.

The profit is the same for 300 rolls that cost $300 as it is for 30 rolls that cost$300.

Let # of rolls = 30
Cost per roll = $10 Day 1: 4/5 of 30, or 24 rolls, are sold at 50 percent above cost --> 1.5($10) = $15 each Total revenue for Day 1: 24 *$15 = $360 Day 2: remaining six rolls are sold at 80 percent of Day 1's price -->$15 * .8 = $12 each Total revenue for Day 2: 6 *$12 = $72 Total revenue for both days =$432

$432 - 300 =$132

Method II - Algebra

xy = 300 = Total cost, where x is unit cost of rolls and y is # of rolls

Day 1 = 4/5y * 3/2x = 6/5xy

Day 2 = 1/5y * (4/5*3/2)x

= 1/5y * 12/10x = 6/25xy

Day 1 + Day 2: 6/5xy + 6/25xy = 36/25xy

xy = 300, so
Total revenue = (36/25)(300) = 432

Total cost = 300
Profit = $132 Answer C _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2570 Re: On a certain day, a bakery produced a batch of rolls at a total produc [#permalink] ### Show Tags 09 Aug 2017, 13:32 1 1 carcass wrote: On a certain day, a bakery produced a batch of rolls at a total production cost of$ 300. On that day, $$\frac{4}{5}$$ of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls?

A. $150 B.$ 144

C. $132 D.$ 108

Profit = $408-$300 = $108 Intern Joined: 18 Aug 2017 Posts: 30 GMAT 1: 670 Q49 V33 Re: On a certain day, a bakery produced a batch of rolls at a total produc [#permalink] ### Show Tags 08 Sep 2017, 22:03 3 chid2 wrote: Can anyone tell me what is wrong with my calculation? carcass Assume batch of rolls =5 Cost per roll =$300/5= $60 First day sales : 4/5*5*$60*1.5 = $360 Second day sales : 1/5*5*$60*0.8 = $48 Total sales =$408
Profit = $408-$300 = $108 Hi, The question stem said that "The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before" So your calculation for second day sale should be 1/5*5*$60*1.5*0.8 = 72.
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Joined: 21 Jun 2017
Posts: 78
Re: On a certain day, a bakery produced a batch of rolls at a total produc [#permalink]

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12 Sep 2017, 08:20
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carcass wrote:
On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, $$\frac{4}{5}$$ of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls? A.$ 150

B. $144 C.$ 132

D. $108 E.$ 90

Since they never give you total amount of rolls produced, just make it 100 rolls, because 100 is an easy number to work with.

Total cost = $300 Total rolls produced = 100$3.00 per roll
50% of $3.00 is$4.50
4/5 of 100 is 80
80 x 4.50 = $360.00 20% of 4.50 =$.90
4.50 - .90 = $3.60 3.60 x 20 =$72.00
$360.00 +$72.00 = $432.00$432.00(revenue) - $300.00(cost) =$132.00 (Profit)

Ans is (C)
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Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39
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On a certain day, a bakery produced a batch of rolls at a total produc [#permalink]

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22 Nov 2017, 09:05
1
1
I cant's understand why we can't just simply find the cost of goods sold at the first day = 240 (4/5=300)
Then add a margin of 1.5, 240*1.5= 360 (sales) and get profit of the 1st day 360-240 = 120
Then why can't we simply apply 0.8 discount (20% off) to the gross margin for the 1st day of 1.5*0.8 and get 1.2
Applying to 1.2 to 60 (cost of goods sold of the 2nd day, which is found as 300*1/5) = 72 (sales)
72-60 = 12 and 120 + 12 = 132
Why do we need to imagine a number of units sold or write equations?
On a certain day, a bakery produced a batch of rolls at a total produc   [#permalink] 22 Nov 2017, 09:05
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