qR from CDM help

[promolion]

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sales tax on sugar is reduced by 20%. if the revenue of the sale of sugar remains unaltered, by what percent must the sales have increased?


A shop keeper unpacks his good to find 6 items missing. he had planned to obtain a sale profit of 10% by selling the good at market price, but now incurs a lost of 5%. how many items did he purchase before they went missing?

Thank you for your time.

 

[Shinpe]

Is that really all the information the problem is providing for the first question? What are the answers? I feel like you need to know what the initial tax was to solve that problem, but I might be wrong. For example if your tax goes from 60% to 40%, then your sales must increase by 1.6/1.4 (14%) while if your tax goes from 30% to 10%, your sales must go up by (1.3/1.1) (18%). So what does CDM say?


For the second question I solved it this way: By losing 6 items, the person basically went from having a return of 1.1*(initial investment I) to 0.95*I so the cost of each item must be (1.1*I - 0.95*I)/6. The cost of each item must also be equal to the initial investment divided by the number of items he bought (I/N). If you set those two equal, after canceling I, you get N=6/0.15=40. Is that what your CDM says?

 

[tsitneD]

whts the answer for number 1

 

[joonkimdds]

common number to pick is hundred so lets say total revenue is 100.
which is selling 10 sugar each for 10 bucks. Now 20% off so make it 8 bucks a sugar but revenue still hundred so (100/8) 12.5 sugar sold.
now the percent up in sale is (12.5-10)/10*100= 25% increase in sale.

AM I CORRECT?

but the problem said tax decreased, not the price of sugar.

 

[tsitneD]

yeah i see that i removed the post. oops

 

[Shinpe]

what happened to the answer to the first one?? This thing is bugging me lol

 

[joonkimdds]

Yah man~ I can't go to sleep!!!! give us the answers!!! ROAR!!!

 

[promolion]

first is 25% and 2nd is 44

 

[joonkimdds]

first is 25% and 2nd is 44

$100 sugar, 100% tax = $200. If tax is reduced by 20%, then it’s $100 sugar and 80% tax = $180.
If 25% is the answer, that means $125 sugar and (125 x 0.8=100 tax) so the total revenue is $225 instead of 200.

I don't understand this.
Does CDM have explanation at all??

 

[tsitneD]

so was I right???????

because thats what i had but i removed the post because the question was very confusing so I later on felt it was wrong.

OR is it different method?

 

[bbwreckerz04]

For the second question I solved it this way.
I pick X equal 10 for easy calculation.

[(11/10)X - (19/20)X]/6 = .25

Then you divide .25 into $11 because that how much profit he was planning to make 10% profit of $10 is $11. I'm not sure how you get 1.

11/.25 = 44

 

[joonkimdds]

what's revenue? is it income + tax?

 

[Shinpe]

For the second question I solved it this way.
I pick X equal 10 for easy calculation.

[(11/10)X - (19/20)X]/6 = .25

Then you divide .25 into $11 because that how much profit he was planning to make 10% profit of $10 is $11. I'm not sure how you get 1.

11/.25 = 44

So what you have is basically (1.1*I-0.95*I)/6 which is the cost of each item, but you set that equal to 0.25. Where did you get 0.25 from???
Also, I tried your answer with numbers. Try it with a cost of $10 or anything. With a $10 cost, and n=44, you'd have total cost $440, and with a 10% profit, you'd have $484 return, and losing 6 items, you'd lose only the cost of those 6 items ($60), not the profit and then you'd have $424 left (aka 96.3%). But if you do it with 40 items (cost $400, with profit $440, losing $60, have 380$(95%) left) then it's right.

Actually, the only way 44 would be right is if you include the profit of those 6 items in your loss (counting your loss as 6*484/440), which I would have to disagree with no matter what CDM says. If you lose 6 goods, you only lose the cost, not the profit, because you never had the profit in the first place to lose it. That's also how you find (1.1*I-0.95*I)/6 to be the cost, because you're assuming when you lose the 6 items, you only lose the cost, not their profit along with them.

I'm not sure if promolion has copied the questions word for word, but I have to say the first one is very badly worded. I still don't see how you can get 25% as an answer. And I still disagree with 44 being the answer, if that's how the question is worded, I think CDM is wrong ;p

 

[bbwreckerz04]

So what you have is basically (1.1*I-0.95*I)/6 which is the cost of each item, but you set that equal to 0.25. Where did you get 0.25 from???
Also, I tried your answer with numbers. Try it with a cost of $10 or anything. With a $10 cost, and n=44, you'd have total cost $440, and with a 10% profit, you'd have $484 return, and losing 6 items, you'd lose only the cost of those 6 items ($60), not the profit and then you'd have $424 left (aka 96.3%). But if you do it with 40 items (cost $400, with profit $440, losing $60, have 380$(95%) left) then it's right.

Actually, the only way 44 would be right is if you include the profit of those 6 items in your loss (counting your loss as 6*484/440), which I would have to disagree with no matter what CDM says. If you lose 6 goods, you only lose the cost, not the profit, because you never had the profit in the first place to lose it. That's also how you find (1.1*I-0.95*I)/6 to be the cost, because you're assuming when you lose the 6 items, you only lose the cost, not their profit along with them.

I'm not sure if promolion has copied the questions word for word, but I have to say the first one is very badly worded. I still don't see how you can get 25% as an answer. And I still disagree with 44 being the answer, if that's how the question is worded, I think CDM is wrong ;p

I got .25 from X=10 which I picked. When you lose an item, you not only lose the cost but the potential profit from its sales. Lets say I buy 10 toys for $10 each to sell for $20 each, and I lose 5 toys. My revenue is only $100 when I could of been $200. God I hope aadsas opens soon, I need to sleep.

 

[Shinpe]

I got .25 from X=10 which I picked. When you lose an item, you not only lose the cost but the potential profit from its sales. Lets say I buy 10 toys for $10 each to sell for $20 each, and I lose 5 toys. My revenue is only $100 when I could of been $200. God I hope aadsas opens soon, I need to sleep.

Can you explain how you're getting 0.25 from your investment = 10???

I guess this depends on how you define the amount that you lose depending on your items. I really do think that when you lose an item you paid 10$ for, you lose 10$, not the 11$ you would have got if you had sold it. It's kind of like poker, you can't lose the money you don't have. When you bet 20$ and then fold with a winning hand, you only lose $20, not the amount of money in the pot since it wasn't yours yet.

 

[bbwreckerz04]

can you explain how you're getting 0.25 from your investment = 10???

I guess this depends on how you define the amount that you lose depending on your items. I really do think that when you lose an item you paid 10$ for, you lose 10$, not the 11$ you would have got if you had sold it. It's kind of like poker, you can't lose the money you don't have. When you bet 20$ and then fold with a winning hand, you only lose $20, not the amount of money in the pot since it wasn't yours yet.

10 is the number of initial item he bought

[(11/10)(10) - (19/20)(10)]/6 = [11 - 9.5]/6 = .25

 

[Shinpe]

10 is the number of initial item he bought

[(11/10)(10) - (19/20)(10)]/6 = [11 - 9.5]/6 = .25

ok so your x is the number of items he bought and you set it equal to 10? First of all, the number of items he bought is the unknown, you can't just set it equal to 10. I believe you mean that 10 is the total money he invested at first because otherwise your equation doesnt make sense. It'd be (110% of the number of items - 95% number of items)/6, which doesnt have a meaning. But saying the money he invested was $10 is i believe what you mean, which makes sense. So doing what you do, you're saying the amount of money he lost for each item is 0.25. Now whether we divide $11 by 0.25 (assuming you also lose the profit) or $10 by 0.25 (assuming you only lose the cost) is the quetion.

I still think it should be 40 items (edit from typo $40), any other thoughts??

 

[bbwreckerz04]

ok so your x is the number of items he bought and you set it equal to 10? First of all, the number of items he bought is the unknown, you can't just set it equal to 10. I believe you mean that 10 is the total money he invested at first because otherwise your equation doesnt make sense. It'd be (110% of the number of items - 95% number of items)/6, which doesnt have a meaning. But saying the money he invested was $10 is i believe what you mean, which makes sense. So doing what you do, you're saying the amount of money he lost for each item is 0.25. Now whether we divide $11 by 0.25 (assuming you also lose the profit) or $10 by 0.25 (assuming you only lose the cost) is the quetion.

I still think it should be $40, any other thoughts??

youre right sorry $10 is the number of money he invested

 

[Streetwolf]

sales tax on sugar is reduced by 20%. if the revenue of the sale of sugar remains unaltered, by what percent must the sales have increased?
tax*sales = revenue (t*s = r)
So now we have 0.8tax instead of just tax because it was reduced by 20%. The revenue remains the same so the sales must be modified by some amount 'x' as such:

0.8t * xs = r
Thus 0.8x = 1 to give us our starting equation of ts=r.
x = 1.25. That means the sales increased by 25%.

A shop keeper unpacks his good to find 6 items missing. he had planned to obtain a sale profit of 10% by selling the good at market price, but now incurs a lost of 5%. how many items did he purchase before they went missing?

Those 6 items together come out to be 15% of what he intended to make (110%). So each one is 2.5% of what he intended to make. Remember that he intended on making 110% (NOT 100%!!!) so 110 / 2.5 = 44 items total.

Thank you for your time.

Answers in bold.

 

[Shinpe]

How is tax*sales = revenue?? Unless you're saying that you bought it at some price and just sold it at the same price while charging tax on it and that tax is your revenue, that equation doesn't work. And this is really not how it's done. If your tax is 60% then you have 0.6*Sales=revenue, but 0.6*sales really just gives you the amount of tax you're charging. So when you sell something, you're really getting 0.6*sales + sales or 1.6* sales back. And if you drop your tax by 20%, your return doesn't drop by 20%, just the tax portion. So you'd have a return of 0.8*0.6*sales + sales, which is not 20% of 1.6* sales.


Either way, I feel like those questions and their answers are poorly worded. I have been tutoring math from algebra to calculus 2 for three years now, and I have to admit, those are one of the most poorly defined problems and use of concepts I have seen in a while. I really hope that the people writing the DAT know math better than people who wrote those CDM questions.

 

[Streetwolf]

Hey I have no idea. The first question does suck, but I know the concept they are testing here, which is why I made up that equation haha. I absolutely see what you are saying about the sales tax. The second question is worded perfectly fine.

 

[Shinpe]

Hey I have no idea. The first question does suck, but I know the concept they are testing here, which is why I made up that equation haha. I absolutely see what you are saying about the sales tax. The second question is worded perfectly fine.

Yea I guess the second question is worded fine. I just think the answer should be $40 not $44. So basically what I'm disagreeing with is I guess the logic used to solve it. I have never seen anyone include a profit that hasn't been made as part of a sell as a loss yet.
Here's different way to say it. When you say he lost 5%. You're counting the money received - money invested. The money he invested would be the 40 items * $10 ($400) in the previous numbers i used and when you say he lost 5%, that means he received $380 back (that doesnt count his profit, because he never got it).
Another thing wrong with your answer is that you're saying that the 6 items were 15% of what he intended to make. No, the items were 15% of what he invested because you calculated it from 110%*investment - 95%* investment. That's not the same as 15% of the 110% (for example instead of making 110, he made 95, so he lost 15$ which is 15% of 100, not 15% of 110).

 

[Streetwolf]

Yea I guess the second question is worded fine. I just think the answer should be $40 not $44. So basically what I'm disagreeing with is I guess the logic used to solve it. I have never seen anyone include a profit that hasn't been made as part of a sell as a loss yet.
Here's different way to say it. When you say he lost 5%. You're counting the money received - money invested. The money he invested would be the 40 items * $10 ($400) in the previous numbers i used and when you say he lost 5%, that means he received $380 back (that doesnt count his profit, because he never got it).
Another thing wrong with your answer is that you're saying that the 6 items were 15% of what he intended to make. No, the items were 15% of what he invested because you calculated it from 110%*investment - 95%* investment. That's not the same as 15% of the 110% (for example instead of making 110, he made 95, so he lost 15$ which is 15% of 100, not 15% of 110).

You are correct, I did mean to say 15% of what he invested. But remember that in calculating the 15%, you have based it off of what he intended to make. He was supposed to make 110% of the money he spent on these things.

For a specific case let's say there were 44 items and he bought all 44 items for $440. His investment is $440. Each item is worth (100/44)% = 2.27% of his investment. Here each item is worth $10. Now he wants to sell them all and in the end make $484. He needs to sell them each for $11 - this is (110/44)% of his investment, or 2.5% each. But he loses 6 of them. That comes out to $66 that he is losing in sales. Instead of making $484 he is only making $418. And 418/440 = 95%. So he's only making 95% of what he spent. Here each item accounts for (95/38)% = 2.5%. The same as before.

In general, let's say he bought 'x' items. Each item is worth (100/x)% of his investment. However he is selling each item for (110/x)% of his investment since he wants to profit 10% of his investment. But then he LOSES 6 items and makes 95% of his investment without those 6 items.

Before the loss: Each item is being sold at 110/x percent of his investment.
After the loss: Each item is being sold at 95/(x-6) percent of his investment.

The two should be equal... the price never changed.

110/x = 95/(x-6)
110(x-6) = 95x
110x - 660 = 95x
15x = 660
x = 44

There are 44 items.

 

[bbwreckerz04]

just study QR from destroyer and kaplan and leave CD to the PAT

 

[Shinpe]

You are correct, I did mean to say 15% of what he invested. But remember that in calculating the 15%, you have based it off of what he intended to make. He was supposed to make 110% of the money he spent on these things.

For a specific case let's say there were 44 items and he bought all 44 items for $440. His investment is $440. Each item is worth (100/44)% = 2.27% of his investment. Here each item is worth $10. Now he wants to sell them all and in the end make $484. He needs to sell them each for $11 - this is (110/44)% of his investment, or 2.5% each. But he loses 6 of them. That comes out to $66 that he is losing in sales. Instead of making $484 he is only making $418. And 418/440 = 95%. So he's only making 95% of what he spent. Here each item accounts for (95/38)% = 2.5%. The same as before.

In general, let's say he bought 'x' items. Each item is worth (100/x)% of his investment. However he is selling each item for (110/x)% of his investment since he wants to profit 10% of his investment. But then he LOSES 6 items and makes 95% of his investment without those 6 items.

Before the loss: Each item is being sold at 110/x percent of his investment.
After the loss: Each item is being sold at 95/(x-6) percent of his investment.

The two should be equal... the price never changed.

110/x = 95/(x-6)
110(x-6) = 95x
110x - 660 = 95x
15x = 660
x = 44

There are 44 items.

You know what? You're right.

I know where I went wrong now. Even though you can't lose the money you don't have, the difference between 110% of investment and 95% of investment does include the profit of those 6 items because 1.1*I include the profit from all items, not just the ones he sold, while the 0.95*I would only include the profit of the items he sold. So this is how I would solve it. 1.1*I-0.95*I = 6 * Cost *1.1, knowing that I = Cost * N, after subs and cancelling C from both sides you'd have 1.1*N-0.95*N = 6 *1.1, which gives N=6*1.1/0.15 = 44.

I still don't have a good feeling about the way you guys are explaining it, other than this last explanation, but hey, whatever works for you ;p

👍

 

[promolion]

Thank you guys. I copied it directly and might miss like an s at the end of a word. There were some other crazy one, but it was pretty long so I refuse to learn it.