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A store currently charges the same price for each towel that

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A store currently charges the same price for each towel that [#permalink] New post 15 Jun 2006, 16:36
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A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
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 [#permalink] New post 15 Jun 2006, 16:45
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C) 3

Given pxq =120 .... (a)

Also (p+1) x (q-10) = 120

i.e. q = 10(1+p)

Replacing q in (a)
p^2+p = 12

or (p+4)(p-3) = 0

i.e p=-4 or 3.
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Re: From Old PowerPrep... [#permalink] New post 15 Jun 2006, 16:50
chiragr wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

A) 1
B) 2
C) 3
D) 4
E) 12



Let current price be x
towels that can be bought with $120 = 120/x

If price is x+1, towels bought = 120/(x+1) = (120/x) - 10
Solving for x yields x=3

Hence C
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 [#permalink] New post 15 Jun 2006, 17:13
Original price = $x

# of towels bought with $120 = 120/x

New price = $(x+1)

# of towels bought with 120 = 120/(x+1) = 120/x - 10
120/(x+1) = (120 - 10x)/x
120x = 120-10x(x+1)
120x = 120x + 120 - 10x^2 -10x
x^2 - x - 12 = 0
(x+4)(x-3) = 0

x = 3


Current price = 3
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 [#permalink] New post 16 Jun 2006, 00:34
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What I did was took numbers and started calculating.......

Equation can be written but since the numbers were small calculating ws easier.

120/3 = 40

New price = 3 + 1 = 4

Number = 120/4 = 30

30 is ten fewer than 40 hence

3 is the intial price
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 [#permalink] New post 16 Jun 2006, 06:32
jaynayak wrote:
What I did was took numbers and started calculating.......

Equation can be written but since the numbers were small calculating ws easier.

120/3 = 40

New price = 3 + 1 = 4

Number = 120/4 = 30

30 is ten fewer than 40 hence

3 is the intial price


My thoughts exactly. I calculated the formula:

120/P = 10+ 120/(P+1) then I started pluggin in numbers since it looked much easier to do then to solve this algebraically.
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 [#permalink] New post 16 Jun 2006, 11:37
"If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax"

Doesn't this mean...

Original N towel, total price X and price of towel is X/N
New N-10 towel, total price 120 and price of towel is X/N+1

How do I conclude that original price X is $120?

If this were to be DS problem I would say that I can not solve this problem with available information.

Any one agrees or I suck in verbal!
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 [#permalink] New post 16 Jun 2006, 12:21
Current:
Price = p
Can be purchased in $120 = 10
So p*n = 120..........Eq1

After increasing price we have (p+1) (n-10) = 120.........Eq2

Solving Eq1 and Eq2 we get p = 3
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Total price [#permalink] New post 26 Aug 2006, 20:32
Chiragr,

120 is not the total price X, it is the amount with which someone can buy n number of towels.

I thought the problem clearly states that... its not to look at the problem so literally I guess :)

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Try this link.. [#permalink] New post 06 Jun 2007, 19:24
http://www.gmatclub.com/phpbb/viewtopic ... ght=towels

I just did a search for towel because I remember seeing this problem before.



For a problem like this you could always start with the answer choices and work backwards if the formula just isn't coming to you.
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 [#permalink] New post 06 Jun 2007, 22:51
C

Let P = price per towel

You can figure that 120/P = the quantity of towels sold.

add 1 to P (price) and you have P+1, which equals the new price per towel.

The new price per towel, P+1, results in 10 fewer towels being purchased for $120. The equation below reflects this:

120/P+1 = 120/P - 10

Now, solve for P.
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Re: Number Properties Question 2 [#permalink] New post 06 Jun 2007, 23:12
700dreamer wrote:
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding tax. What is the current price of each towel?

A) $1
B) $2
C) $3
D) $4
E) $12


Current price of each towel = $x

Number of current towels which can be bought for $120 is equal to (120/x)

Increased current price = $x + $1

[(120/x)-(10)]*(x+1) = 120

becomes a quadratic equation : x^2 + x-12 = 0

(x+4)(x-3) = 0

thus x=3

C is the answer.
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Re: 200. current price [#permalink] New post 23 Feb 2008, 19:37
i get C, 3 dollars.

let old price = x, therefore new price is x+1

amount of towels you could buy with old price is 120/x, and amount with new price is (120/x+1)-10

set these equations equal to each other, and solve for x. youll end up with a quadratic with roots -4 and 3. -4 is inadmissable, so 3 is your answer.

try it out: for 120 dollars, you can get 40 towels at 3 bucks a pop. Now, for a dollar increase, i.e. 4 dollars, you can get only 30 towels. Thats a difference of 10 towels due to a $1 increase in price.
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Re: OG - PS 200 [#permalink] New post 02 Mar 2008, 08:37
C

Here is what I have done...

Assuming n-no of towels, x-unit price of towel before increase:

n*x=120
(n-10)*(x+1)=120

You could solve the equations, but I tried different values of n ending with 0 from 120's prime factors - 5*3*2*2*2
so n could be 20, 30, 40 and corresponding x values are 6,4 and 3. And 40 and 3 satyisfy the second condition, so 3 is the answer.
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Re: What is the most efficient way to solve this problem- Ideas? [#permalink] New post 22 Jun 2008, 07:58
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this question is actually very simple and can be best approached by trying numbers..

so suppose orig.price=3..then 120/3=40 towels
increase it by 1=new price=4 120/4=30 towels..


another hint that you want to look for is that 120..what ever numbers you look for must be factors of 120..

in our case that doesnt help since all of them are factors of 120.
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Re: Algebra Applied [#permalink] New post 16 Sep 2010, 06:35
Expert's post
Baten80 wrote:
OG 195. A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $ 12

Suggest shortest way to solve the problem.


Let the current price be p and the # of towels sold at this price be n. Then we would have two equations:

pn=120 amd (p+1)(n-10)=120 at this point you can solve the system of equations for p (you'll get quadratic equation to solve) or try to substitute answer choices.

When substituting answer choices it's good to start with the middle value, so in our case C - $3 --> so if p=3 then 3n=120 --> n=40 --> (3+1)(40-10)=4*30=120, so this answer works.

Answer: C.

Hope it helps.
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Re: Algebra Applied [#permalink] New post 17 Sep 2010, 18:19
I felt using answer choices was fast....surely less than minute.

A. With $1, 120 towels, after price increase 60 towels....
B 60 towels and then 30
C. 40 and then 30 towels....-> answer
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Re: PS numbers [#permalink] New post 08 May 2011, 09:55
carollu wrote:
A store currently charges the smae price for each towel that it sells. if the current price of each towel were to be increased by 1.10 fewer of the towels could be bought for 120, excluding sales tax. what is the current price of each towel?

a)1 b)2 c)3 d)4 e)12


I think there ought to be a comma between 1 and 10 here. If that were the case, we know that increasing price by 1 reduces volume by 10 for a fixed budget of 120. If initial price is x and volume y then we have

xy = 120

(x+1)*(y-10)=120

120 is 3*4*10

So, we can deduce that if x is 3 then y is 40 and when x+1 becomes 4, y-10 becomes 30 and hence x is 3 - Answer C
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Re: PS numbers [#permalink] New post 08 May 2011, 11:52
Assuming n towels are bought and price of each towel is x.
n.x=120
price increase x+1
total towels that can be bought = n-10
now (n-10)(x+1)=120

Solving 2 equations --> x=(n-10)/10
Substituting answers, only x=3 solves the problem

Answer C
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Re: PS numbers [#permalink] New post 08 May 2011, 13:21
i agree with @beyongmat.. about the typo in question. there has to be a comma after 1.

=> 120 = ((120/x)-10)(x+1)

=> x =3

Answer is C.
Re: PS numbers   [#permalink] 08 May 2011, 13:21
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