A marketer bought N crates of empty cardboard gift boxes. Each crate

Question

A marketer bought N crates of empty cardboard gift boxes. Each crate held Q individual gift boxes, and the lot of N crates was purchases at a wholesale price of W dollars. This marketer will sell collections of J cardboard gift boxes to retailers, at a price of P dollars for each collection. (Note: J is a divisor of Q.) The marketer knows that, when he has sold all the cardboard gift boxes this way, he wants to net a total profit of Z dollars on the entire transaction. What price P must he charge, to net this profit? Express P in terms of N, Q, W, J, and Z.

A. J(Z - W)/(NQ)
B. J(Z + W)/(NQ)
C. Q(Z - W)/(NJ)
D. Q(Z + W)/(NJ)
E. N(Z - W)/(QJ)

Kudos for a correct solution.

A. J(Z - W)/(NQ)
B. J(Z + W)/(NQ)
C. Q(Z - W)/(NJ)
D. Q(Z + W)/(NJ)
E. N(Z - W)/(QJ)

GMATinsight · Accepted Answer

The marketer initially paid W= cost.

There are Q boxes in each crate, and J boxes make a collection,

so there are Q/J collections in each crate, and NQ/J collections in total.

If he charges a price P, his revenue would be PNQ/J.

Now, profit = revenue - cost,

so Z = PNQ/J – W

i.e. P = (Z+W)J / NQ

Answer: Option  B

LaxAvenger · Answer

J (W) / (NQ) should be price to break even.
Add Z and it should be price to net the profit

-->
Option B should be price to net the profit.

Answer is B

PareshGmat · Answer

Answer = B. J(Z + W)/(NQ)

Total Profit = Z

Total cost price = w

Total boxes = nq

Selling price per box  =\frac{p}{j}

Total selling price  = \frac{p}{j} * nq

Setting up the profit equation

z = \frac{pnq}{j} - w

p = \frac{z+w}{nq} * j

EMPOWERgmatRichC · Answer

Hi All,

This question is wordy and loaded with variables, but it can be solved by TESTing VALUES. There are some fantastic 'shortcuts' in the the answer choices as well.

We're told that there are N crates and that each crate holds Q gift boxes.

N = 3 crates
Q = 4 gift boxes/crate
(3)(4) = 12 total gift boxes

We're told that all of the crates were purchased for a total of W dollars

W = 12
12 gift boxes for 12 dollars

The seller will sell J gift boxes per 'collection' at a price of P dollars per 'collection' (we're told that J is DIVISOR of Q)

J = 2 gift boxes per 'collection'
12/2 = 6 'collections available

P = 3 dollars per 'collection'
(6)(3) = $18 in revenue after ALL collections|gift boxes are sold

Total profit is Z dollars
$18 in revenue
$12 cost
$18 - $12 = $6 = Z

We're asked for the value of P, using the other variables....

N = 3
Q = 4
W = 12
J = 2
Z = 6

We're looking for an answer that equals 3.

Now, before jumping into the answer choices, notice all of the PATTERNS that exist:
1) Answers A and B are almost exactly the same.
2) Answers C and D are almost exactly the same.
3) Each parentheses is either (Z+W) or (Z-W)

You can use the patterns to avoid doing the same calculation over and over. Let's start with Answers A and B:

A= 2(-6)/12 = -1 NOT a match
B= 2(18)/12 = 3 This IS a match

Now, let's do C and D tougher (note that we ALREADY KNOW the values of Z+W and Z-W from our prior work):

C= 4(-6)/6 = -4 NOT a match
D= 4(18)/6 = 12 NOT a match

E= 3(-6)/8 = -18/8 NOT a match

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION Algebraic Solution: So, the marketer initially paid W: that was his outlay, his cost. There are Q boxes in each crate, and J boxes make a collection, so there are Q/J collections in each crate, and NQ/J collections in total. If he charges a price P, his revenue would be PNQ/J. Now, profit equals revenue minus cost, so Z = PNQ/J – W . Solve this for P gpp-vitac_img7.png Numerical Solution: Here, we have several choices to make, and it would be a good idea to pick numbers that aren’t the same, or aren’t even divisible by each other if that’s not required. Picking some different prime numbers is good way eliminate more than one answer that comes out to the correct value. I will say the price is 2, a nice round prime number. Let’s say J = 3, so Q must be a multiple of that — say Q = 30. Let’s N = 7. This means he has 10 collections from every box, and 70 collections from the total lot. If he charges $2 per collection, that’s a revenue of $140. Let’s say his outlay was W = $95; then his profit is Z = $45. OK, that’s an unusual enough set of number that we expect no more than one solution will work. We will plug in N = 7, Q = 30, W = 95, J = 3, and Z = 45, and we hope to get an output of P = 2. gpp-vitac_img8.png Thus, because we chose numbers well, the only possible answer is (B). - See more at: https://magoosh.com/gmat/2014/gmat-pract ... QEkpA.dpuf

stclark3 · Answer

In the Algebraic solution the Equation is set up as

(PNQ)/J = Z + W

What clues in the question signal that you should'nt perform operations on Z or W?

I was setting up the cost as W*N, the number of crates times the cost.

ThatDudeKnows · Answer

Plenty of solid solutions above for both the algebraic and plugging in approaches. Good stuff! But let's say that you get stuck with the algebra, or that you try plugging in and find that more than one answer choice works for your numbers and you don't want to invest more time into trying even more numbers, or that you just decide quickly that this question is going to take a while and you think you'll be better off guessing and saving the time for other questions. I've found that a lot of the questions that have a bunch of variables often times line up really well with what you'd guess if you use a little logic...not always, but you're probably improving your odds a LOT from 1-out-of-5 that you'd have from random guessing. Okay, so let's look at the question. - We are told that J is a divisor of Q. They probably tell us that fact because we will NEED Q to be a multiple of J. I'm more likely to lean toward an answer choice with Q being divided by J. C and D seem better than the other three answer choices. - We are trying to find what P we have to charge to get Z profit. Our net INCOME is Z and our EXPENSE is W. Seems more likely that we will have Z rather than -Z and that we will have -W rather than W. A, C, and E sound better than B and D. Only C fits both of those. Well, wouldn't you know...?!?

No math. Just logic. Right answer. 20 seconds.

priyanshi123t · Answer

another way to solve this is by checking the answer choices 
as for b it comes to ,
no of items sold (J) x ( profit(z) + cost (w) )/ total i.e. no of crates * no of items per crate

Aabhash777 · Answer

N = No. of Empty Crates
Q = Individual Gifts in each of N Crates
NQ costs = $W
J = No. of N sold
Z = Profit
P = Price needed

Total Cost = $W
Total Profit = $Z

Total Sales = W+Z (Cost + Profit)

P needed = J(W+Z) / NQ

pmahaja2 · Answer

C is incorrect, corrct answer is B

A marketer bought N crates of empty cardboard gift boxes. Each crate

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A marketer bought N crates of empty cardboard gift boxes. Each crate

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