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A certain grocery purchased x pounds of produce for p dollar

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A certain grocery purchased x pounds of produce for p dollar [#permalink]

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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)

Problem Solving
Question: 171
Category: Algebra Simplifying algebraic expressions; Applied problems
Page: 84
Difficulty: 600


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

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

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New post 17 Mar 2014, 03:21
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Profit = S.P. - C.P.
C.P. = xp
S.P. = (x-y)s

Profit = (x-y)s -xp

Either I am doing something wrong here or this sum is overly simple

Answer - A
Time Taken - 1:18 (I thought there is a catch in this sum so spent a lot of time)
Difficulty level - 500

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

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New post 18 Mar 2014, 01:24
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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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New post 18 Mar 2014, 07:23
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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)

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A certain grocery purchased x pounds of produce for p dollar [#permalink]

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New post 25 Mar 2015, 08:06
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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New post 25 Mar 2015, 11:34
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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:
[Reveal] Spoiler:
A


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

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New post 23 Mar 2017, 10:15
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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New post 27 Mar 2017, 16:32
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]

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New post 27 Mar 2017, 19:04
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]

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New post 20 Dec 2017, 01:01
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] 20 Dec 2017, 01:01
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