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A store currently charges the same price for each towel that [#permalink]
 15 Jun 2006, 17:36
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69% (02:54) correct
30% (01:53) wrong based on 1 sessions
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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VP
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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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Director
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Re: From Old PowerPrep... [#permalink]
15 Jun 2006, 17:50
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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GMAT Club Legend
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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
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SVP
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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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Manager
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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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Senior Manager
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"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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CEO
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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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Manager
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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
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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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Director
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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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Director
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Re: Number Properties Question 2 [#permalink]
07 Jun 2007, 00:12
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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Intern
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HELP ME.
A store currently charge the same price of a towel that it sells.If the current price is to be increased by $1. 10 fewer of the towels could be bought for $120. What is the current price?
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Regards,
Sonfbm
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Manager
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It's kinda hard to know exactly what the question is asking bc you have some grammatical errors...can you re-state the question exactly how it is written in the text/program?
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Manager
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I thought the answer was 3, because i picked a low number and figured it out.
Would you mind showing how you set up your equation, sonfbm?
Thanks
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Senior Manager
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simonsanchez wrote: I thought the answer was 3, because i picked a low number and figured it out.
Would you mind showing how you set up your equation, sonfbm?
Thanks
If the current price is x, then
120/x = 120/(x+1) + 10
x = 3.
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Re: 200. current price [#permalink]
23 Feb 2008, 20:37
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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Senior Manager
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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]
22 Jun 2008, 08:58
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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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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.
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