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# A store currently charges the same price for each towel that

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Re: PS numbers [#permalink]  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

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Re: PS numbers [#permalink]  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

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Re: PS numbers [#permalink]  08 May 2011, 19:36
let price for each towel = x

then 120/x = number of towels purchased.

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

substituting x = 3, LHS = RHS = 30 .

Hence C.
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Re: PS numbers [#permalink]  11 May 2011, 04:09
n*p = (n - 10)(p+1)

np = 120

120 = (120/p - 10) (p+1)

120p = (120 - 10p)(p+1)

12p = (12-p)(p+1)

Checking the values, p = 3

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Re: 600-700 level question [#permalink]  04 Oct 2011, 20:29
To solve algebraically, set up two equations and then set them equal to one another.

p = price of towel
t = number of towels

Equation 1) pt = 120 => p = 120/t
Equation 2) (p + 1) * (t - 10) = 120

pt = (p + 1) * (t - 10)
pt = pt - 10p + t - 10
10 = -10p + t
10 = -10 * (120 / t) + t
10t = -1200 + t^2
t^2 - 10t - 1200 = 0
(t + 30) * (t - 40) = 0
t = - 30 or t = 40

Since t is the number of towels, it can only be a positive number, and thus t = 40. Since you want the current price of each towel, or p, divide 120 by 40 (equation 1) to get p = 3.

Alternatively, you can also plug in the answer choices to avoid algebra.

pt = 120

A) p = 1; t = 120
B) p = 2; t = 60
C) p = 3; t = 40
D) p = 4; t = 30
E) p = 12; t = 10

Just from that, you can tell that by increasing the price by $1 from$3 to $4, 10 fewer towels can be bought for$120. Thus the answer is C.
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Re: 600-700 level question [#permalink]  04 Oct 2011, 23:41
Good solutions sesamemochi, but I'd like to modify it slightly to make it faster to solve. From my experience, I would say that we must always try to form an equation in the variable that we need to calculate. This will save us one step at the end. For example, I would solve this problem as below -

Assume the current price to be x. So, as per the given information, we can form the below equation -
120/x = 120/(x+1) + 10

Solving this equation for x, we get 3 and -4
Choose 3 as price cannot be negative.

Secondly, for your alternate 'value plugging' approach, time can be saved if only the options with consecutive prices are considered. In this case 1, 2, 3, 4. But since 12 is not in the sequence, there was no need to even consider option E.

Lastly, in most cases, I find plugging of values a risky affair. Even plugging requires thinking, for example in this case even after plugging the values, only the results of consecutive price pairs matter, such as 1,2 ; 2,3 and 3,4. And imagine if option D was 5 instead of 4, then the plugging would have been useless. Moreover if someone does all the plugging and calculations and later realizes that there are no consecutive pairs to consider, it will be such a waste of time.
My 2 cents - All in all, I suggest that we use value plugging as the last resort. It is more important to know the concepts. Value plugging needs thinking too, so better apply thoughts to applying the concepts.
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Re: A store currently charges the same price for each towel that [#permalink]  24 Mar 2012, 13:51
I don't understand how do you come from pxq =120 to (p+1) x (q-10) = 120

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Re: A store currently charges the same price for each towel that [#permalink]  24 Mar 2012, 14:00
Expert's post
Stiv wrote:
I don't understand how do you come from pxq =120 to (p+1) x (q-10) = 120

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

"If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for$120": $$pn=120$$ amd $$(p+1)(n-10)=120$$, so the same $120 can buy $$n$$ towels for $$p$$ each or $$n-1$$ towels for $$(p+1)$$ each. For complete solution check this: a-store-currently-charges-the-same-price-for-each-towel-that-30571-20.html#p782872 Hope it helps. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 6784 Followers: 369 Kudos [?]: 83 [0], given: 0 Re: A store currently charges the same price for each towel that [#permalink] 15 Sep 2013, 18:35 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 21 Aug 2013 Posts: 113 Schools: ISB '15 Followers: 2 Kudos [?]: 16 [0], given: 60 Re: A store currently charges the same price for each towel that [#permalink] 01 Mar 2014, 03:54 Hi, I know this is a OG question. Still from the below text how can we assume that the current P X Q = 120. 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? _________________ Veritas Prep - 650 MGMAT 1 590 MGMAT 2 640 (V48/Q31) Please help the community by giving Kudos. Math Expert Joined: 02 Sep 2009 Posts: 29856 Followers: 4924 Kudos [?]: 53965 [0], given: 8260 Re: A store currently charges the same price for each towel that [#permalink] 01 Mar 2014, 05:49 Expert's post seabhi wrote: Hi, I know this is a OG question. Still from the below text how can we assume that the current P X Q = 120. 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? The price increase and quantity decrease are linked with the amount of$120, how else?

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-store-currently-charges-the-same-price-for-each-towel-that-144780.html
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Re: A store currently charges the same price for each towel that   [#permalink] 01 Mar 2014, 05:49

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