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

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Joined: 02 Sep 2009
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A marketer bought N crates of empty cardboard gift boxes. Each crate  [#permalink]

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18 Feb 2015, 04:26
1
9
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Difficulty:

75% (hard)

Question Stats:

60% (02:52) correct 40% (02:47) wrong based on 116 sessions

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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.

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Re: A marketer bought N crates of empty cardboard gift boxes. Each crate  [#permalink]

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18 Feb 2015, 06:40
1
Bunuel wrote:
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)

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

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A marketer bought N crates of empty cardboard gift boxes. Each crate  [#permalink]

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18 Feb 2015, 11:23
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Bunuel wrote:
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.

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.

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Re: A marketer bought N crates of empty cardboard gift boxes. Each crate  [#permalink]

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18 Feb 2015, 21:19
1
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

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

$$p = \frac{z+w}{nq} * j$$
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Re: A marketer bought N crates of empty cardboard gift boxes. Each crate  [#permalink]

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18 Feb 2015, 22:05
1
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
(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

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Math Expert Joined: 02 Sep 2009 Posts: 49303 Re: A marketer bought N crates of empty cardboard gift boxes. Each crate [#permalink] ### Show Tags 22 Feb 2015, 12:14 Bunuel wrote: 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. 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 Attachment: gpp-vitac_img7.png [ 2.46 KiB | Viewed 2300 times ] 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.
Attachment:

gpp-vitac_img8.png [ 15.7 KiB | Viewed 2300 times ]

Thus, because we chose numbers well, the only possible answer is (B).

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Re: A marketer bought N crates of empty cardboard gift boxes. Each crate  [#permalink]

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05 Aug 2018, 12:39
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.
Re: A marketer bought N crates of empty cardboard gift boxes. Each crate &nbs [#permalink] 05 Aug 2018, 12:39
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# A marketer bought N crates of empty cardboard gift boxes. Each crate

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