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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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Answer = A

Weight.................... Cost................. Total
x ............................ p........................ xp

Spoiled:
y................................p.........................yp

Sold
(x-y)..........................s ............................ (x-y)s


Profit = (x-y)s - xp
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

(A) (x- y)s - xp
(B) (x- y)p- ys
(C) (s - p)y - xp
(D) xp - ys
(E) (x- y)(s- p)


Given that cost of x pounds of produce for p dollars per pound

Or, Cost of produce = xp

Produce that is sold = x pounds of produce - y pounds that is discarded

Given that, Selling Price is s dollars per pound

So, Selling Price of (x-y) pounds of produce = (x-y)s

Gross Profit = Selling Price - Cost = (x-y)s - xp

Answer: (A)

Difficulty Level: 550
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
Just as a quick tip, since Profit = Total Revenue - Total Cost

And we know his total cost is xp, we can eliminate 3 answers right away, just by reading the first sentence
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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Hi All,

While this question is 'thick', it can be solved with note-taking, TESTing VALUES and some basic arithmetic."

We're told that "A certain grocery purchased X pounds of produce for P dollars per pound."

X = 2 pounds of produce
P = 3 dollars per pound (cost)
So (2)(3) = $6 was spent to buy this produce

Next, we're told that "Y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for S dollars per pound...."

Since we only had 2 pounds of produce to begin with, and we still need to sell some produce.....

Y = 1 pound of produce spoiled
S = 7 dollars per pound (sell price or remaining produce)
So (7)(2-1) = $7 revenue from selling the 'good' produce

We're asked for the GROSS PROFIT on the sale of the produce. $7 - $6 = $1 of gross profit.

While the answer choices look 'thick', they actually have several 'pieces' in common, so you can use that to your advantage (notice how XP and (X-Y) show up several times - you can do each of those calculations ONCE and then plug the result into multiple answers and save some time).

Answer A: (1)(7) - (2)(3) = 7-6 = 1 This IS a match
Answer B: (1)(3) - (1)(7) = negative. Not a match.
Answer C: (4)(1) - 6 = negative. Not a match
Answer D: 6 - 7 = negative. Not a match
Answer E: (1)(4) = 4. Not a match

Final Answer:

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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
this is a words to math task
((x-y)*s-x*p)/x*p
Answer is A
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

(A) (x- y)s - xp
(B) (x- y)p- ys
(C) (s - p)y - xp
(D) xp - ys
(E) (x- y)(s- p)


The cost to the grocery was xp dollars. Since y pounds were discarded, x - y was actually sold at a price of s dollars, and thus the revenue earned was s(x - y) dollars.

Thus, the gross profit was s(x - y) - xp dollars.

Answer: A
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
The total cost = (number of pounds)*(price per pound) = xp;
The total revenue = (number of pounds)*(price per pound) = (x - y)s.

The gross profit = (x - y)s - xp.

Answer: A.
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
Bunuel wrote:
SOLUTION

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

(A) (x- y)s - xp
(B) (x- y)p- ys
(C) (s - p)y - xp
(D) xp - ys
(E) (x- y)(s- p)

The total cost = (number of pounds)*(price per pound) = xp;
The total revenue = (number of pounds)*(price per pound) = (x - y)s.

The gross profit = (x - y)s - xp.

Answer: A.

Trick is here that E is a good answer if you believe that spoilage is not part of cost of goods sold and should be out of equation. In fact, I believe that gross profit is revenue minus cost of goods sold and I would put spoilage to the other line
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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Hi,

I was able to get A, but my first initial reaction was to also subtract yp (price of spoilage and the dollars per pound that was used to purchase it)

Can someone help me realize why this "cost" is not part of the gross profit equation?

Thank you
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
take any three values which obey the above condition and put those values in options you will get correct answer.
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
Hello,

X=total quantity
Y=spoiled quantity
P=cost
S=sale

total Revenue=(X-Y)S
total cost= XP

gross profit= (X-Y)S-XP
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
Expert Reply

Solution



Given:
    • A certain grocery purchased x pounds of produce for p dollars per pound.
    • y pounds of the produce had to be discarded due to spoilage.
      o And, remaining were sold for s dollars per pound.

To find:
    • The option that correctly represents the gross profit on the sale of the produce.

Approach and Working:
    • Cost price =$x * p
    • Selling price =$(x-y) * s
      o Profit = (x-y) *s – x *p

Hence, the correct answer is option A.

Answer: A
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

(A) (x- y)s - xp
(B) (x- y)p- ys
(C) (s - p)y - xp
(D) xp - ys
(E) (x- y)(s- p)


Cost price = x*p
y pounds of the produce had to be discarded due to spoilage
--> Utilized qty = x - y
Selling price = (x - y)*s

--> Profit = SP - CP = (x - y)*s - x*p

IMO Option A

Pls Hit Kudos if you like the solution
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
total cost = xp
total revenue = (x-p)s

gross profit : (x-p)s - xp

Answer is A.
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

(A) (x- y)s - xp
(B) (x- y)p- ys
(C) (s - p)y - xp
(D) xp - ys
(E) (x- y)(s- p)


Cost price \(= xp\)

Grocery left after discard \(= x-y\)

Sales revenue of the rest of the grocery \(= (x-y)s\)

Profit=Sales revenue- cost

\(=(x-y)s-xp \)

The answer is A
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]
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Re: A certain grocery purchased x pounds of produce for p dollar [#permalink]