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Judy bought a quantity of pens in packages of 5 for $0.80 per package

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Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400

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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 23 Jul 2017, 15:36
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carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


It should be D.

Cost price per pen = $0.80 / 5 = $0.16 or 16 cents.
Sale price per pen = $0.60 / 3 = $0.20 or 20 cents.
Profit per pen = 0.20 - 0.16 = $0.04 or 4 cents.

Profit = Profit per pen x number of pens

number of pens = Profit/profit per pen = 8/0.04 = 200
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Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 23 Jul 2017, 15:59
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carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400

carcass, you are a master of crafty language, and this one takes the prize.

The trap is in the second sentence: "She sold all of the pens in packages of 3 for $0.60 per package."

That sentence does not mean that all the pens she sold were in packages of 3. In fact, coupled with the implication of answers that are not multiples of 15, the sentence means just the opposite; it means "not all the pens sold were in boxes of 3."

A quantity that can be divided evenly into 5 per package and into 3 per package must be divisible by 15. None of the answer choices offers that possibility.

So the pens Judy sold were not all in packages of 3.

We have total profit. To get the number of pens, we need Judy's cost per pen and her sell price per pen.

A package of five pens cost Judy 80 cents. \(\frac{80}{5}\) = each pen cost 16 cents.

A package of three pens sold for 60 cents.\(\frac{60}{3}\) = each pen sold for 20 cents.

Profit per pen is 20 - 16 = 4 cents' profit per pen.

Total profit = (profit per pen) * (number N of pens sold)

$8.00 = ($0.04)N

\(\frac{$8.00}{($0.04)}\) = 200

Number of pens sold: 200

Answer D
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 23 Jul 2017, 16:17
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carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40
B. 80
C. 100
D. 200
E. 400

I. Cost per pen = 0.80/5 = (4/5)/5 = (4/5)*(1/5) = 4/25 = 16/100 = 0.16;
II. Revenue per pen = 0.60/3 = 6/30 = 1/5 = 0.20;
III. Profit per pen = Revenue per pen - Cost per pen = 0.20 - 0.16 = 0.04;
IV. Total profit = profit per pen * quantity of pens: (8) = (0.04) * quantity, quantity = 8/0.04 = 800/4 = 200.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 23 Jul 2017, 23:48
2
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


Cost price: packages of 5 for $0.80 per package = $0.80/5 = $0.16 per pen.
Selling price: packages of 3 for $0.60 per package = $0.60/3 = $0.2 per pen.

Profit = ¢4 per pen.
Total profit = ¢800.
The number of pens = 800/4 = 200.

Answer: D.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 24 Jul 2017, 08:21
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\(\frac{x}{5} * (0.8) - \frac{x}{3}*(0.6)\) = 8

\(\frac{2.4x - 3x}{15} = 8\)

x=200
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 24 Jul 2017, 09:14
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


CP of a pen = \(\frac{80}{5} = 16\)

SP of a pen = \(\frac{60}{3} = 20\)

Profit = \(20-16 = 4\), per pen.

Total profit = \(800\), so number of pens = \(\frac{800}{4} = 200\). Ans - D.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 26 Jul 2017, 15:37
1
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400


We can let x = the number of pens she bought and sold. Since she bought the pens in packages of 5, she bought x/5 packages. Similarly, since she sold the pens in packages of 3, she sold x/3 packages. She bought the packages at $0.80 each and sold them at $0.60 each, and her profit is $8.00; thus, we can create the following equation:

0.60(x/3) - 0.80(x/5) = 8.00

60(x/3) - 80(x/5) = 800

20x - 16x = 800

4x = 800

x = 200

Answer: D
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Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 05 Sep 2017, 07:35
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400



Profit = revenue - cost; Revenue = Sales price x quantity; cost = buy price x quantity
profit = profit per individual pen x total number of pens

Saleprice/pen = 0.60/3 = .20 cents per pen
Buyprice/pen =0.80/5 = .16 cents per pen on the buy
profit per pen = .20 - .16 = .04 cents profit per pen

Profit = profit per pen x number of pens bought and sold
8.00 = .04 x N
200 = number of pens bought and sold

bottom line with this one is to start out finding the cost of individual pen and the sale of individual pen. once you find the individual profit, set your variable, and divide from the total profit given.

I got this one right, but idk, something weird with the way it is worded threw me off balance for a bit.
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Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 22 Nov 2017, 22:59
Bunuel wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400

Cost price: packages of 5 for $0.80 per package = $0.80/5 = $0.16 per pen.
Selling price: packages of 3 for $0.60 per package = $0.60/3 = $0.2 per pen.

Profit = ¢4 per pen.
Total profit = ¢800.
The number of pens = 800/4 = 200.

Answer: D.


Bunuel ScottTargetTestPrep how is it possible to sell 200 pens in packages of 3? shouldn't the number of pens be a multiple of 3?
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Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post Updated on: 25 Nov 2017, 06:37
mnshg wrote:
how is it possible to sell 200 pens in packages of 3? shouldn't the number of pens be a multiple of 3?

chetan2u VeritasPrepKarishma mikemcgarry may you please help clarify my doubt?
I was solving this Q under timed conditions.
I approached the problem by concluding that the answer must a multiple of 3 and 5, but couldn't find such a number in the answer choices. So I got tensed about the time wasted and then couldn't solve it any further.

Originally posted by mnshg on 25 Nov 2017, 06:26.
Last edited by mnshg on 25 Nov 2017, 06:37, edited 1 time in total.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 25 Nov 2017, 06:36
mnshg wrote:
mnshg wrote:
how is it possible to sell 200 pens in packages of 3? shouldn't the number of pens be a multiple of 3?

chetan2u VeritasPrepKarishma mikemcgarry may you please help clarify my doubt?



Hi,

you are correct the number of pens should have been a multiple of 3...
I can always take it as the remaining 2 were not sold...

Although answer can be found without getting into number of packages and thus avoiding looking into this aspect, but it is not exactly correct even if it is an official Q
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 15 Dec 2017, 09:42
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400



--> cost price of 5 pens is 0.8 => 15 would cost 2.4$
---> selling price of 3 pens is 0.8 => 15 would cost 3.0$
Net profit on 15 pens is 0.6 $
0.6 $ profit on 15 pens
8.0$ profit on how many pens = (8 *15)/(0.6) = (800* 15)/(60) = (800/4)= 200.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 13 Oct 2018, 12:58
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400



This question has to be flawed. You can't have 200/3 or 66 2/3 packages sold, and you can't assume 2 pens were not sold either, because the stem specifically states that all pens were sold.
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Re: Judy bought a quantity of pens in packages of 5 for $0.80 per package  [#permalink]

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New post 31 Oct 2018, 14:32
LEOiAM wrote:
carcass wrote:
Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

A. 40

B. 80

C. 100

D. 200

E. 400



This question has to be flawed. You can't have 200/3 or 66 2/3 packages sold, and you can't assume 2 pens were not sold either, because the stem specifically states that all pens were sold.

I don't normally stick my nose in the quant section of the forum much, but a very smart tutor I work with brought up the same concern yesterday.

generis does a nice job of addressing this worry in this post above -- and for whatever it's worth, this is an official question, so if it's flawed, we're stuck with it, anyway. :)

If it helps, I'll try to rephrase what generis said above. In the original question, Judy bought pens (200 of them, as it turns out) in packages of 5. "She sold all of the [200] pens in packages of 3 for $0.60." Technically speaking, she must have sold at least 201 pens in those packages of 3, because 200 isn't divisible by 3. But that doesn't change the fact that she sold "all of the [200] pens" for $0.20 per pen. She must have sold some additional pens as well, but that doesn't change the fact that she sold those 200 pens that she bought for a profit of $8.

So for the question to make sense, you don't have to assume that she sold only 198 pens -- because the question clearly states that she sold ALL of the pens she bought in those packs of 5. But there's no reason why she couldn't sell additional pens to bring the total up to a multiple of 3. So she still makes a profit of 4 cents per pen for all 200 pens.

So technically speaking, the question isn't flawed or wrong. I think that the question could have been clearer and better if they'd chosen better numbers, but GMAC doesn't care what I think. :)

I hope this helps!
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