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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]

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27 Dec 2012, 05:47
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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 Kudos [?]: 3453 [0], given: 0 Math Expert Joined: 02 Sep 2009 Posts: 41873 Kudos [?]: 128579 [3], given: 12180 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 27 Dec 2012, 05:49 3 This post received KUDOS Expert's post 11 This post was BOOKMARKED Walkabout 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 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 $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. _________________ Kudos [?]: 128579 [3], given: 12180 Intern Joined: 11 Apr 2013 Posts: 2 Kudos [?]: 7 [3], given: 4 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 18 Oct 2013, 09:32 3 This post received KUDOS 1 This post was BOOKMARKED I thought it would be easier to just use a smart number. I picked the middle number option (C)$3 per towel and proceeded to divide $120 with$3 to make 40 towels.
Then I tried with (D) $4 which gave me 30 towels. Therefore the current price must be$3

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Economist GMAT Tutor Instructor
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Re: A store currently charges the same price for each towel that [#permalink]

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19 Oct 2013, 09:23
psychedelictwirl wrote:
I thought it would be easier to just use a smart number.
I picked the middle number option (C) $3 per towel and proceeded to divide$120 with $3 to make 40 towels. Then I tried with (D)$4 which gave me 30 towels.
Therefore the current price must be $3 Answer: C. I agree. I think this problem is a textbook example for why reverse plugging in is a valuable strategy. _________________ Economist GMAT Tutor http://econgm.at/econgmat (866) 292-0660 Kudos [?]: 46 [0], given: 7 Intern Joined: 04 Aug 2013 Posts: 6 Kudos [?]: 5 [0], given: 8 Concentration: Sustainability, Entrepreneurship WE: Architecture (Energy and Utilities) Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 30 Oct 2013, 06:45 1 This post was BOOKMARKED N = total no. of towel P = Price of towel NP=120…(1), ; N = 120/p (N-10)(P+1) = 120…(2) From 2, NP+N-10P-10=120 120/P*P + 120/P -10P = 130 (Plugging from 1) 120/P -10P = 10 P^2+P-12 = 0 (P+4)(P-3)=0 Hence, P=3 (As price cannot be negative) *This is indeed the long method, but I am comfortable with algebra, than plugging no.) Kudos [?]: 5 [0], given: 8 Senior Manager Joined: 23 Oct 2010 Posts: 382 Kudos [?]: 392 [0], given: 73 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 20 Nov 2013, 05:29 (P+1)(N-10)=NP N-10P-10=0 NP=120 => N=P/120 N-10P-10=0 P^2+P-12=0 P=3 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Kudos [?]: 392 [0], given: 73 Senior Manager Joined: 28 Apr 2014 Posts: 273 Kudos [?]: 40 [3], given: 46 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 15 May 2014, 10:27 3 This post received KUDOS 1 This post was BOOKMARKED Bunuel wrote: Walkabout 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 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 $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. Bunuel Instead of two variables p,n cant it be solved in 1 variable as below Say p = original price of 1 towel so 120/p = 120/(p+1) + 10 putting values from options gives the value of p=3 Kudos [?]: 40 [3], given: 46 Math Expert Joined: 02 Sep 2009 Posts: 41873 Kudos [?]: 128579 [0], given: 12180 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 16 May 2014, 01:26 himanshujovi wrote: Bunuel wrote: Walkabout 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 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 $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. Bunuel Instead of two variables p,n cant it be solved in 1 variable as below Say p = original price of 1 towel so 120/p = 120/(p+1) + 10 putting values from options gives the value of p=3 Yes, that's correct. _________________ Kudos [?]: 128579 [0], given: 12180 Intern Joined: 05 Feb 2014 Posts: 15 Kudos [?]: [0], given: 18 Location: India Concentration: Human Resources, General Management Schools: Tepper '20 (S) GMAT 1: 720 Q49 V40 GPA: 3.33 Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 17 Sep 2014, 10:07 Bunuel wrote: Walkabout 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 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 $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. Hi Bunnel How is pn=120 first equation ?? Kudos [?]: [0], given: 18 Math Expert Joined: 02 Sep 2009 Posts: 41873 Kudos [?]: 128579 [0], given: 12180 A store currently charges the same price for each towel that [#permalink] ### Show Tags 17 Sep 2014, 11:22 SunthoshiTejaswi wrote: Bunuel wrote: Walkabout 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 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 $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. Hi Bunnel How is pn=120 first equation ?? If the current price of each towel were to be increased by$1 (the current price p, new price p+1), 10 fewer of the towels (n for the current number of towels, n-10 for new number of towels) could be bought for $120. So, for$120 for the current price p, we can buy n towels: pn=120.
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Re: A store currently charges the same price for each towel that [#permalink]

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17 May 2016, 04:50
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Expert's post
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 Solution: We can start by creating some variables. Q = quantity of towels sold P = price per towel sold Next we can set up some equations. We know that at the current price: PQ = 120 We are next given that if the current price of each towel were to be increased by$1, 10 fewer of the towels could be bought for $120. From this we can say: (P + 1)(Q – 10) = 120 Since we need to determine the value of P, we should get the second equation in terms of P only. We can do this by manipulating the equation PQ = 120. So we can say: Q = 120/P Now we can plug in 120/P for Q in the equation (P + 1)(Q – 10) = 120. We now have: (P + 1)(120/P – 10) = 120 FOILing this, we get: 120 – 10P + 120/P – 10 = 120 –10P + 120/P – 10 = 0 We can multiply the entire equation by P to get rid of the denominators. This gives us: –10P^2 + 120 – 10P = 0 10P^2 + 10P – 120 = 0 P^2 + P – 12 = 0 (P + 4)(P – 3) = 0 P = -4 or P = 3 Since P can’t be negative, P = 3. Answer is C. _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Kudos [?]: 827 [1], given: 5 Manager Joined: 30 Dec 2015 Posts: 90 Kudos [?]: 20 [1], given: 153 GPA: 3.92 WE: Engineering (Aerospace and Defense) Re: A store currently charges the same price for each towel that [#permalink] ### Show Tags 16 Oct 2016, 19:19 1 This post received KUDOS Walkabout 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 the original cost of towels = x

$$\frac{120}{x}- \frac{120}{(x+1)} = 10$$
$$120 = 10(x^2 + x)$$
($$x^2 + x -12) = 0$$
$$(x+4)(x-3)=0$$
x=3
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Re: A store currently charges the same price for each towel that [#permalink]

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01 Oct 2017, 00:59
I understand pn = 120 but doesn't (p+1)(n−10)=120 assume that the new price divides 120 evenly? What if that is not the case?

Obviously in this problem it does divide evenly but what about a similar problem where the new price leaves us with some some money left over < p? Shouldn't the second equation be an inequality or something to do with remainders?

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Re: A store currently charges the same price for each towel that [#permalink]

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01 Oct 2017, 04:19
ThisandThat wrote:
I understand pn = 120 but doesn't (p+1)(n−10)=120 assume that the new price divides 120 evenly? What if that is not the case?

Obviously in this problem it does divide evenly but what about a similar problem where the new price leaves us with some some money left over < p? Shouldn't the second equation be an inequality or something to do with remainders?

We are told that "If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for$120", so $120 is exactly how much you need to buy 10 fewer of the towels if the price of each towel were to be increased by$1.
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Re: A store currently charges the same price for each towel that   [#permalink] 01 Oct 2017, 04:19
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# A store currently charges the same price for each towel that

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