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A store currently charges the same price for each towel that

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Senior Manager
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A store currently charges the same price for each towel that [#permalink]

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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 [Reveal] Spoiler: OA VP Joined: 02 Jun 2006 Posts: 1267 Followers: 2 Kudos [?]: 78 [2] , given: 0 [#permalink] Show Tags 15 Jun 2006, 16:45 2 This post received KUDOS 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. Director Joined: 16 Aug 2005 Posts: 945 Location: France Followers: 1 Kudos [?]: 23 [0], given: 0 Re: From Old PowerPrep... [#permalink] Show Tags 15 Jun 2006, 16:50 1 This post was BOOKMARKED 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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15 Jun 2006, 17:13
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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 SVP Joined: 30 Mar 2006 Posts: 1737 Followers: 1 Kudos [?]: 76 [3] , given: 0 [#permalink] Show Tags 16 Jun 2006, 00:34 3 This post received KUDOS 1 This post was BOOKMARKED 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 Manager Joined: 10 May 2006 Posts: 186 Location: USA Followers: 1 Kudos [?]: 5 [0], given: 0 [#permalink] Show Tags 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. Senior Manager Joined: 05 Jan 2006 Posts: 382 Followers: 1 Kudos [?]: 83 [0], given: 0 [#permalink] Show Tags 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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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 _________________ SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008 Manager Joined: 09 Aug 2005 Posts: 72 Followers: 1 Kudos [?]: 2 [0], given: 0 Total price [#permalink] Show Tags 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 MG Intern Joined: 22 Mar 2007 Posts: 47 Followers: 0 Kudos [?]: 0 [0], given: 0 Try this link.. [#permalink] Show Tags 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. Director Joined: 12 Jun 2006 Posts: 532 Followers: 2 Kudos [?]: 116 [0], given: 1 [#permalink] Show Tags 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]

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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. SVP Joined: 28 Dec 2005 Posts: 1575 Followers: 3 Kudos [?]: 144 [0], given: 2 Re: 200. current price [#permalink] Show Tags 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]

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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]

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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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16 Sep 2010, 06:35
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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.

Hope it helps.
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17 Sep 2010, 18:19
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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 _________________ If you like my post, consider giving me some KUDOS !!!!! Like you I need them Manager Joined: 14 Feb 2011 Posts: 196 Followers: 4 Kudos [?]: 124 [0], given: 3 Re: PS numbers [#permalink] Show Tags 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 Intern Joined: 29 Mar 2011 Posts: 20 Followers: 0 Kudos [?]: 3 [0], given: 0 Re: PS numbers [#permalink] Show Tags 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 Director Joined: 01 Feb 2011 Posts: 757 Followers: 14 Kudos [?]: 114 [0], given: 42 Re: PS numbers [#permalink] Show Tags 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 Go to page 1 2 Next [ 31 posts ] Similar topics Replies Last post Similar Topics: 1 A departmental store charges the commission of 15 percent on the first 5 30 May 2016, 12:17 Laura took out a charge account at the General Store and agreed to pay 1 24 Mar 2016, 01:58 4 The price of a coat in a certain store is$500. If the price of the co 7 17 Jun 2015, 21:26
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