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Manager  Joined: 02 Dec 2012
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A store currently charges the same price for each towel that  [#permalink]

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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 Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 58445 Re: A store currently charges the same price for each towel that [#permalink] Show Tags 8 18 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. _________________ Most Helpful Community Reply Intern  Joined: 11 Apr 2013 Posts: 2 Re: A store currently charges the same price for each towel that [#permalink] Show Tags 4 2 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

General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: How does GMAT translate "increased by X%"?  [#permalink]

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StormedBrain wrote:
omohojo wrote:
I have been getting confused in how to convert the term "increased X%" into a formula.

Is "increased by X%" interpreted as:

$$\frac{100+X}{100}$$

OR

$$\frac{1+X}{100}$$

OR

$$1+X$$

Problem Example:
If the price increased by X% from 2001 to 2002 and by Y% from 2002 to 2003, what is the percentage increase from 2001 to 2003?

Whenever we say , X% increase ....it means an increase of x per 100.

So result will be (100 + 100*(x/100)) or 100+X .

Increased by x% means increase by (1+x/100) times.

For example, if the original value is 100 and x=10%, then the final value is 100*(1+10/100)=110.

Check here: http://gmatclub.com/forum/how-does-gmat ... l#p1269316

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

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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 Intern  Joined: 04 Aug 2013 Posts: 5 Concentration: Sustainability, Entrepreneurship WE: Architecture (Energy and Utilities) Re: A store currently charges the same price for each towel that [#permalink] Show Tags 2 2 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.) Senior Manager  Joined: 23 Oct 2010 Posts: 323 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 2 (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 Manager  Joined: 28 Apr 2014 Posts: 195 Re: A store currently charges the same price for each towel that [#permalink] Show Tags 4 1 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 Math Expert V Joined: 02 Sep 2009 Posts: 58445 Re: A store currently charges the same price for each towel that [#permalink] Show Tags 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. _________________ Intern  B Joined: 05 Feb 2014 Posts: 15 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 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 ?? Math Expert V Joined: 02 Sep 2009 Posts: 58445 A store currently charges the same price for each towel that [#permalink] Show Tags 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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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. _________________ Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Manager  S Joined: 30 Dec 2015 Posts: 82 GPA: 3.92 WE: Engineering (Aerospace and Defense) Re: A store currently charges the same price for each towel that [#permalink] Show Tags 4 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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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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Posts: 58445
Re: A store currently charges the same price for each towel that  [#permalink]

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A store currently charges the same price for each towel that  [#permalink]

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Hi All,

Most GMAT questions can be solved in a variety of ways, so you should look for alternatives to "math" approaches (in many cases, the math approach takes the longest to set up and complete).

Here, we're essentially asked to spend $120 on towels. We're then asked to figure out the price point at which ADDING$1 to the price of a towel results in 10 FEWER towels purchased. Since the answers are NUMBERS (and almost all consecutive integers), we can TEST THE ANSWERS....

IF....
Towels are....
$1 each, then we can buy 120 towels$2 each, then we can buy 60 towels
$3 each, then we can buy 40 towels$4 each, then we can buy 30 towels
$5 each, then we can buy 24 towels Now, stop and look at the progression. We're looking for a point at which the DIFFERENCE is 10 towels. That only happens in one "spot" - when the price is increased from$3 to $4. The question asks for the current (re: lower) price. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ IIMA, IIMC School Moderator V Joined: 04 Sep 2016 Posts: 1366 Location: India WE: Engineering (Other) A store currently charges the same price for each towel that [#permalink] Show Tags 1 Bunuel niks18 similar query as Walkabout Quote: 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.

is this because of: A store currently charges the same price for each towel that it sells.
What am I missing?
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Re: A store currently charges the same price for each towel that  [#permalink]

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Bunuel niks18

similar query as Walkabout

Quote:
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. is this because of: A store currently charges the same price for each towel that it sells. What am I missing? Hi adkikani Here important point to note is that total expenses before and after changing the price remain same i.e$120.

so if earlier price was p and total quantities bought was n, then net cost will be pn=120

after change in price and quantity also the expense remain same, hence we get (p+1)*(n-10)=120
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Re: A store currently charges the same price for each towel that  [#permalink]

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niks18

Quote:
Here important point to note is that total expenses before and after changing the price remain same i.e $120. Is this distinctly mentioned anywhere or you inferred the same? Let me dissect sentence wise to understand: Quote: A store currently charges the same price for each towel that it sells. Let there be x towels in store, this sentence means that if p is price for each towel then px is price for total no of towels. Quote: 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 (p+1)*(x-11) = 120$120 is the amount after the decrease in quantity and price increase.

From where did you infer px=120 from the two statements?

Should not correct way be:
A store currently charges total of $120and 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 I am assuming sales tax is simply given for confusion. _________________ It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!! Retired Moderator D Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 A store currently charges the same price for each towel that [#permalink] Show Tags 3 adkikani wrote: niks18 Quote: Here important point to note is that total expenses before and after changing the price remain same i.e$120.

Is this distinctly mentioned anywhere or you inferred the same?

Let me dissect sentence wise to understand:

Quote:
A store currently charges the same price for each towel that it sells.

Let there be x towels in store, this sentence means that if p is price for each towel
then px is price for total no of towels.

Quote:
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

(p+1)*(x-11) = 120
$120 is the amount after the decrease in quantity and price increase. From where did you infer px=120 from the two statements? Should not correct way be: A store currently charges total of$120and 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

I am assuming sales tax is simply given for confusion.

Here's the question stem

"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?"

now read this part carefully -

"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."

Why is 120 mentioned here? what is the constraint with 120? for example price is increased so could be the quantity resulting in a different total cost. But why 120?

For eg. if the price of 1 pen is 9 and you bought 10 pens, your total cost is 90. Now you increase the price of pen by 1 i.e new price of pen is 10 so with this 90 you will be able to buy 9 pens only. This is same as saying "If the current price of each pen were to be increased by $1, 1 fewer of the pens could be bought for$90, excluding sales tax."

Kindly read the sentence multiple times to understand the language. the current price is not directly mentioned but you can surely arrive at it from the second sentence. A store currently charges the same price for each towel that   [#permalink] 06 Jan 2018, 20:30

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