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A store currently charges the same price for each towel that

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

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New post 26 Mar 2018, 10:43
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.



To whom it may concern :)

This is to testify that i dont i understand the following :)

here \((p+1)(n-10)=120\) where from do we get +1 and -10 ? :? whats the logic ?

we know that cost is insresed by 1.10 and another value we have is 120 ....

i sincerely dont understand the solution written by Zeus-Bunuel :)

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

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New post 26 Mar 2018, 12:17
1
dave13 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.



To whom it may concern :)

This is to testify that i dont i understand the following :)

here \((p+1)(n-10)=120\) where from do we get +1 and -10 ? :? whats the logic ?

we know that cost is insresed by 1.10 and another value we have is 120 ....

i sincerely dont understand the solution written by Zeus-Bunuel :)

please help:)


Hi dave13

What we need to understand is if there are n towels being sold and the cost of a towel is p, n*p = 120$

We are given this part in the question stem
If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120

Cost of towel goes up by 1 (p + 1) when there are 10 fewer towels bought (n-10) for the same $120
So basically the overall cost remains the same even though costs go up by $1 and the number of
towels reduce by 10

Therefore, we write (p+1)*(n-10) = 120

Hope that helps you!
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New post 26 Mar 2018, 12:21
pushpitkc
oh i misread the question i thought priced increased by 1.1 (by 1 dollar and 10 cents :) )
many thanks for clarification! :)
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New post 26 Mar 2018, 12:49
JeffTargetTestPrep 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


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.



JeffTargetTestPrep hello :) hope my question finds you well :-)

what rule did you use that you changed places of values and its signs ? :?

from this –10P^2 + 120 – 10P = 0

to this 10P^2 + 10P – 120 = 0

pushpitkc any idea how ? :)
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New post 27 Mar 2018, 01:19
1
dave13 wrote:
JeffTargetTestPrep 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


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.



JeffTargetTestPrep hello :) hope my question finds you well :-)

what rule did you use that you changed places of values and its signs ? :?

from this –10P^2 + 120 – 10P = 0

to this 10P^2 + 10P – 120 = 0

pushpitkc any idea how ? :)



Hey dave13

This equation \(-10P^2 + 120 – 10P = 0\) is nothing but -(\(10P^2 + 10P - 120\) = 0)

When we multiply both the sides by -1, we get \(10P^2 + 10P - 120 = 0\)

Hope this helps you!
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New post 27 Mar 2018, 09:15
dave13 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.

@dave13 wrote:To whom it may concern :)

This is to testify that i dont i understand the following :)

here \((p+1)(n-10)=120\) where from do we get +1 and -10 ? :? whats the logic ?

we know that cost is insresed by 1.10 and another value we have is 120 ....

i sincerely dont understand the solution written by Zeus-Bunuel :)

please help:)

dave13 , you wanna testify, do you? Better not let me get you on cross-ex. :lol: I'll do direct examination instead. In this Wonderland court I can lead my own witness and I can testify.

Bunuel is NOT working directly with a percent increase multiplier. How about (my witness!) we strike that from the record.

He does not have to work with a multiplier, because we have an actual dollar value increase AND the actual decrease in the # of towels.

+1 means = + $1 per towel
-10 means = we can buy 10 fewer towels than we could at the lower price

The logic? We have an original equation and a new equation.
The new equation expresses the increase in price (+$1) and the decrease in quantity (-10)

The original equation:
p = price of each towel
n = number of towels
p*n = Total Price

(Ex.: p=$2, n=10. Ten towels at $2 ea = p*n = $20)

--Price goes UP by $1? That's just (p + $1)
--# of towels at that price DECREASES by 10? That's (n-10) towels

If price per towel goes up, you can buy fewer towels than the original # of towels, because RHS total price stays the same.

You can only spend $120.

Originally, p*n = 120
Then price changes.
Now you have increased price per towel (p + $1)
And we are GIVEN the decreased # of towels: (n-10 towels)

p * n = $120 (Original)
(p + 1)(n - 10) = $120 (New)
Don't solve the equations

Put the answer choices into them.
--For the answer choice, use (p*n) to find original # of towels
--Then use second equation with increased price to find new # of towels

Use ONLY (p) and (p+1). Solve for # of towels, n

Let's try D) $4 = current price
How many towels can we buy at $4 ea?
p * n = $120
$4 * n = $120
n = 30 towels

Price goes UP by $1.
Now each towel costs $(p+1)=($4+1)= $5
How many can we buy for $5 each?
$5 * n = $120
n = 24 towels

Before we could buy 30. Now we can buy 24. That's SIX fewer towels. Not 10 fewer. WRONG.

Try C) $3 is current price
How many towels can we buy at $3 each?
$3 * n = $120
n = 40 towels

Price increases by $1. $(p+1) =$(3+1)= $4
How many towels can we buy at $4 each?
$4 * n = $120
n = 30

Before, we could buy 40. Price increased. Now we can buy only 30. How many fewer towels at higher price? (40-30)= 10 fewer towels
Bingo. Answer C

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

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New post 23 Jun 2019, 07:12
WillEconomistGMAT wrote:
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.



Can you please explain the question by this strategy.
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Re: A store currently charges the same price for each towel that  [#permalink]

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New post 23 Jun 2019, 14:04
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Hi AmanMatta,

This question can certainly be solved by TESTing THE ANSWERS (a Tactic in which you 'plug in' answers to see if they "fit" the given information; even when an answer doesn't fit, you can often determine whether that answer is 'too big' or 'too small' and narrow down the remaining possibilities).

Here, we're told that a certain number of towels can be bought for $120 and that increasing the price of a towel by $1 will decrease the total number of towels purchased by 10. We're asked for the CURRENT price of a towel. Let's start by TESTing Answer B:

Answer B: $2

If the current price is $2, then we can buy $120/$2 = 60 towels
Increasing the price to $3 means that we could then buy $120/$3 = 40 towels
That's a decrease of 20 towels, which is NOT a match (it's supposed to be 10 towels). We need the difference to be SMALLER, so we need fewer towels at each step. Let's raise the price....

Answer D: $4

If the current price is $4, then we can buy $120/$4 = 30 towels
Increasing the price to $5 means that we could then buy $120/$5 = 24 towels
That's a decrease of 6 towels, which is NOT a match (it's supposed to be 10 towels). We need the difference to be BIGGER, so we need more towels at each step - and we should lower the price. There's only one answer left that makes sense...



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

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New post 13 Sep 2019, 05:14
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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


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

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New post 08 Mar 2020, 19:50
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


Method 1: Quadratic

120/P - 120/(P+1) = 10
(120P + 120 - 120P)/(P(P + 1)) = 10
12 = P(P + 1)

Approach 1:
P(P +1) = 12
Working backwords: 3 * 4 = 12 => ANSWER: 3

Approach 2:
P^2 + P - 12 = 0
(P + 4) (P - 3) = 0
P = 3

Method 2: Working Backwords

B) 120/2 = 60; 120/3 = 40; Gap = 20 => Not the answer
D) 120/4 = 30; 120/5 = 24; Gap = 6 => Not the answer

C) 120/3 = 40; 120/4 = 30; Gap = 10 => Answer
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Re: A store currently charges the same price for each towel that  [#permalink]

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New post 19 Apr 2020, 22:52
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

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, Bunuel, chetan2u, IanStewart, ArvindCrackVerbal, AaronPond, GMATinsight

It seems that the current price could be also \($-4\). How the two different prices ($3 and $-4) effect whole the SAME scenario?
Thanks__
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Re: A store currently charges the same price for each towel that  [#permalink]

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New post 19 Apr 2020, 23:59
1
Asad 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

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, Bunuel, chetan2u, IanStewart, ArvindCrackVerbal, AaronPond, GMATinsight

It seems that the current price could be also \($-4\). How the two different prices ($3 and $-4) effect whole the SAME scenario?
Thanks__


Asad

When we get some results with quadratic, then we need to use the basic understanding of given variables

e.g. Price can NOT be negative
e.g. In work rate problems, the number of men/machines can NOT be negative and also can NOT be decimal numbers

Here we have to use the same logic and strike off the negative value and accept the positive possible values.

I hope this explains your doubt. :)
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New post 20 Apr 2020, 07:20
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Asad wrote:
It seems that the current price could be also \($-4\). How the two different prices ($3 and $-4) effect whole the SAME scenario?
Thanks__


If the price of a towel was negative 4 dollars, that would mean the store is giving you $4 every time you buy a towel. So with $120, you could buy an infinite number of towels. In that case, if the store 'increases' the price by $1, the number of towels you can buy is still infinite, so the price can't be negative $4, since that wouldn't agree with the information in the question -- you wouldn't then be able to buy "10 fewer towels" when the price goes up.

Prices and quantities of things need to be positive (or possibly zero in rare cases) on the GMAT.
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New post 20 Apr 2020, 08:39
Hi there Walkabout

This is a good Problem Solving question testing the concept of 'Linear and Quadratic Equations'.

Per the question stem, the amount spent on purchase of towels in both the situations = $120

Let's assume the current price per towel = x
Further let quantity bought for $120 = y
Thus, xy = 120

As per question stem,
If price of each towel is increased by $1, total quantity bought for $120 = 10 less than earlier = y - 10
Thus, 120 = (x+1).(y-10)
==> 120 = xy -10x + y -10
==> 120 = 120 - 10x +y -10 {xy = 120}
==> 10x = y - 10
Substituting y = 120/x:
10 x = (120/x) - 10
\(==> 10 {x^2} = 120 - 10x
==> {x^2} = 12 - x
==> {x^2} + x -12 = 0\)
==> (x+4).(x-3) = 0
x= -4, 3
Because x can't be negative, current price per towel =x = 3

Answer (C)
Hope this was elaborate enough.
What do you think?

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

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

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New post 21 Apr 2020, 04:47
1
Asad 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

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, Bunuel, chetan2u, IanStewart, ArvindCrackVerbal, AaronPond, GMATinsight

It seems that the current price could be also \($-4\). How the two different prices ($3 and $-4) effect whole the SAME scenario?
Thanks__


Hello Asad,

You are to find out the current price of each towel. The ‘P’ represents the current price of each towel.
Quantities like price, distance, area etc., cannot be negative. It defies logic. And logic is one of the essential pillars of Math.

As such, although you obtain 3 and -4 as the solutions for the Quadratic equation, you will have to tag the constraint to these values to figure out that -4 is not a possible solution in the given context.

The context defined in the question should also be taken into consideration while solving a problem. And that is why it’s emphasized by many experts that you shouldn’t rely on Math alone while solving a GMAT Quant question. These questions also test your ability to apply sound logic while arriving at an answer.

However, when you solve this question using the options, you will end up understanding your own answer better and will not have doubts about the validity of the answer. That’s why I recommend using the answer options to solve the question, especially when you have 5 clear numbers.

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

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New post 21 Apr 2020, 21:55
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Asad 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

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, Bunuel, chetan2u, IanStewart, ArvindCrackVerbal, AaronPond, GMATinsight

It seems that the current price could be also \($-4\). How the two different prices ($3 and $-4) effect whole the SAME scenario?
Thanks__


Did this question come to your mind because futures on crude oil has gone into negative territory? :)

Note that it is because companies have run out of storing capacity for any crude oil possession in the future and will need to invest a whole lot more in creating more storage. The same will not be applicable to towels on a shelf in the supermarket. They will sooner throw them away than pay you money to take them home! :)
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Re: A store currently charges the same price for each towel that   [#permalink] 21 Apr 2020, 21:55

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A store currently charges the same price for each towel that

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