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OG 12 ed: towels question

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OG 12 ed: towels question

by singhpreet1 » Thu Jun 24, 2010 10:34 pm
OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12

[spoiler]OA: A[/spoiler]

i could not make head or tail of this question. would highly appreciate a detailed step by step explanation of this.

thanks. Preet
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by kvcpk » Thu Jun 24, 2010 11:12 pm
Let the current price of each towel be x
Let the number of towels sold be y

Then current revenue is xy = 120

when price becomes x+1, towels sold were y-10
But the revenue was still xy=120

So (x+1)(y-10) = xy = 120
So xy -10x +y -10 = 120
-10x+y-10 = 0
y = 10x+10

sub this in xy=120

x(10x+10) = 120
x^2 +x -12 = 0
(x+4)(x-3) = 0

Therefore x=3

Answer should be C
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by singhpreet1 » Thu Jun 24, 2010 11:20 pm
kvcpk wrote:Let the current price of each towel be x
Let the number of towels sold be y

Then current revenue is xy = 120

when price becomes x+1, towels sold were y-10
But the revenue was still xy=120

So (x+1)(y-10) = xy = 120
So xy -10x +y -10 = 120
-10x+y-10 = 0
y = 10x+10

sub this in xy=120

x(10x+10) = 120
x^2 +x -12 = 0
(x+4)(x-3) = 0

Therefore x=3

Answer should be C
makes a bit of sense though still not completely..will review your explanation again..

yes i accept and apologize for posting the wrong answer choice..it is indeed C. sorry for the typo.

thanks.
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by kvcpk » Thu Jun 24, 2010 11:30 pm
No Problem!!

Let me know in case you face any difficulty understanding it.
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by GMATGuruNY » Fri Jun 25, 2010 2:34 am
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12
When a question asks for a specific amount (in this case, the current price of each towel), you can just try each answer choice until you find the one that works.

We should start with answer choice C, because it's right in the middle. Answer choice C says that each towel is $3:

If each towel is $3, then $120 will get us 120/3 = 40 towels.
If the price per towel is increased by $1, then each towel will be 3 + 1 = $4 per towel.
If each towel is $4, then $120 will get us 120/4 = 30 towels.

Are we able to buy 10 fewer towels? Yes. Then answer choice C works.

The correct answer is C.
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by sanju09 » Fri Jun 25, 2010 3:21 am
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12

[spoiler]OA: A[/spoiler]

i could not make head or tail of this question. would highly appreciate a detailed step by step explanation of this.

thanks. Preet

I have problem in the bold part above. I think a comma separation must have been there to avoid any mystification. Well, this is the kind of problem where we really don't need to do much of Algebra on the main test. They want you to exercise their most favorite trick called "Pick and Plug". Remember, as the choices are in an order and the circumstantial number behavior is in your mind, always start from C, if it works, bingo, if not, then you are at least sure whether to look up or down of C as per the circumstantial number behavior.

So try C. $3 first!

In $120, one can buy 40 towels @ $3 per towel, but when $3 is increased to $4, $120 can now buy 30 towels, which is 10 fewer of the towels could be bought for $ 120 earlier.

[spoiler]It worked!

C[/spoiler]
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by singhpreet1 » Fri Jun 25, 2010 3:26 am
GMATGuruNY wrote:
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12

When a question asks for a specific amount (in this case, the current price of each towel), you can just try each answer choice until you find the one that works.

We should start with answer choice C, because it's right in the middle. Answer choice C says that each towel is $3:

If each towel is $3, then $120 will get us 120/3 = 40 towels.
If the price per towel is increased by $1, then each towel will be 3 + 1 = $4 per towel.
If each towel is $4, then $120 will get us 120/4 = 30 towels.

Are we able to buy 10 fewer towels? Yes. Then answer choice C works.

The correct answer is C.
i missed the all important que in the question and misread all along for so much time, i thought it said that the price was increased by $1.10, rather than if the price was increased by $1, 10 fewer could be bought! Gosh...i need to be careful...and a lesson for everyone else how you can mess the simplest question and create havoc for yourself

Preet
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by real2008 » Fri Jun 25, 2010 5:16 am
Please type questions correctly so that others don't get confused......However, I am highlighting the error in typing if I am correct in my assumption..... I hope it is by 1$, 10 fewer
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12

[spoiler]OA: A[/spoiler]

i could not make head or tail of this question. would highly appreciate a detailed step by step explanation of this.

thanks. Preet
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by GMATGuruNY » Fri Jun 25, 2010 5:36 am
singhpreet1 wrote:
GMATGuruNY wrote:
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12

When a question asks for a specific amount (in this case, the current price of each towel), you can just try each answer choice until you find the one that works.

We should start with answer choice C, because it's right in the middle. Answer choice C says that each towel is $3:

If each towel is $3, then $120 will get us 120/3 = 40 towels.
If the price per towel is increased by $1, then each towel will be 3 + 1 = $4 per towel.
If each towel is $4, then $120 will get us 120/4 = 30 towels.

Are we able to buy 10 fewer towels? Yes. Then answer choice C works.

The correct answer is C.
i missed the all important que in the question and misread all along for so much time, i thought it said that the price was increased by $1.10, rather than if the price was increased by $1, 10 fewer could be bought! Gosh...i need to be careful...and a lesson for everyone else how you can mess the simplest question and create havoc for yourself

Preet
An instructive reminder:

Many "math" mistakes are really reading mistakes.

If you ever get confused, reread the question. You might have misread or misunderstood something important. There's a big difference between increasing the price of each towel by $1 and increasing it by $1.10, much more than the decimal .10 would suggest. Those 10 cents matter!
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by atg212 » Wed Aug 04, 2010 1:12 pm
Thanks GURU, your plug method saved me a lot of time on this one...otherwise its a multiple step algebraic solve that would have taken too much time.

Best,
T
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by rahul goyal » Wed Aug 11, 2010 10:56 pm
GMATGuruNY wrote:
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12
When a question asks for a specific amount (in this case, the current price of each towel), you can just try each answer choice until you find the one that works.

We should start with answer choice C, because it's right in the middle. Answer choice C says that each towel is $3:

If each towel is $3, then $120 will get us 120/3 = 40 towels.
If the price per towel is increased by $1, then each towel will be 3 + 1 = $4 per towel.
If each towel is $4, then $120 will get us 120/4 = 30 towels.

Are we able to buy 10 fewer towels? Yes. Then answer choice C works.

The correct answer is C.
Thanks GMATGuruNY.Your explanation is very clear.
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by billnepill » Tue Feb 01, 2011 5:29 am
Hi, guys

Sorry if my question comes across stupid, but how do we know the revenue is 120 ?

Q stem says : 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.

From this info I could infer the equation (n-10)(p+1)= 120, where p is the current price and n is the number of towels before they were decreased.

How do we infer pn=120, that is, the current revenue is 120? We are given a hypothetical revenue if the price were increased and the number decreased.

Maybe it's obvious, but atm I cannot see where that info came from. Could someone elaborate?

Thanks. Kudos
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by GMATGuruNY » Tue Feb 01, 2011 7:32 am
billnepill wrote:Hi, guys

Sorry if my question comes across stupid, but how do we know the revenue is 120 ?

Q stem says : 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.

From this info I could infer the equation (n-10)(p+1)= 120, where p is the current price and n is the number of towels before they were decreased.

How do we infer pn=120, that is, the current revenue is 120? We are given a hypothetical revenue if the price were increased and the number decreased.

Maybe it's obvious, but atm I cannot see where that info came from. Could someone elaborate?

Thanks. Kudos
10 fewer than what? 10 fewer than the number that could be purchased for $120 at the current price. Hence we can derive the two equations that you indicated above.

I would argue that plugging in the answer choices is much safer and faster.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

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by billnepill » Thu Feb 03, 2011 4:14 am
GMATGuruNY wrote:
billnepill wrote:Hi, guys

Sorry if my question comes across stupid, but how do we know the revenue is 120 ?

Q stem says : 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.

From this info I could infer the equation (n-10)(p+1)= 120, where p is the current price and n is the number of towels before they were decreased.

How do we infer pn=120, that is, the current revenue is 120? We are given a hypothetical revenue if the price were increased and the number decreased.

Maybe it's obvious, but atm I cannot see where that info came from. Could someone elaborate?

Thanks. Kudos
10 fewer than what? 10 fewer than the number that could be purchased for $120 at the current price. Hence we can derive the two equations that you indicated above.

I would argue that plugging in the answer choices is much safer and faster.
Hi,

Apparently, in problems of this kind RC skills are as important as math skills.

The wording of the problem above and its logic are unnatural to me, but I will work on it.

Btw, in order for the plug-in strategy to work, one has to understand that part well, too. The information about the current revenue is needed in both solutions.

Anyways, thanks a lot!
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by Abhishek009 » Thu Feb 03, 2011 4:57 am
GMATGuruNY wrote:
singhpreet1 wrote:OG 12 ed: page180 q. 195

A store currently charges the same price for each towel that is 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
5. $12
When a question asks for a specific amount (in this case, the current price of each towel), you can just try each answer choice until you find the one that works.

We should start with answer choice C, because it's right in the middle. Answer choice C says that each towel is $3:

If each towel is $3, then $120 will get us 120/3 = 40 towels.
If the price per towel is increased by $1, then each towel will be 3 + 1 = $4 per towel.
If each towel is $4, then $120 will get us 120/4 = 30 towels.

Are we able to buy 10 fewer towels? Yes. Then answer choice C works.

The correct answer is C.

I found this the best shortcut , still there is one more way of solving this problem:

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

After some logical steps:

x^2 +x - 12 = 0

Now x will be either +3 or -4

Since price can't b -ve the price of each towel is $3
Abhishek
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