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

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.

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.

\(\frac{x}{5} * (0.8) - \frac{x}{3}*(0.6)\) = 8

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

x=200

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.

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

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?

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.

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

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!

The first thing I did was determine the least common multiple of 5 and 3 which ends up being 15. You then multiple the 5 pen package cost of $0.80 by 3 to arrive at $2.40 per 15 pens and then you multiply the 3 pen selling price of $0.60 by 5 to arrive at $3.00 per 15 pens. Now you can calculate the profit for 15 pens ($3.00 - $2.40 = $0.60).

This next piece has been key for me especially for questions such as these. As someone who isn't always comfortable with setting things up algebraically, I'll often plug and chug with easy numbers. For this problem I asked myself, "what if I multiplied the $0.60 by 10 to arrive at $6.00 profit for 150 pens. From here the intuitive jump to 200 given the other option of 400 is incredibly reasonable and gets me to D without anymore math.

I fully acknowledge that this approach is likely not for everyone, but I wanted to share how I've solved similar problems in short order.

Bunuel are we not suppose to assume number of pens in a package?

If we say 5 pens for $0.80, then price per pen will be 0.80/5


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

I might be missing your point but "5 for $0.80 per package" means that each pen cost $0.80/16 = $0.16.