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Towells trick

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by Mormuse » Mon Apr 08, 2013 4:48 am
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

The OG solution is tricky, is there any other way of dealing with this problem?
Thx
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by Anju@Gurome » Mon Apr 08, 2013 4:57 am
claudayst 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?
You can try plugging the options as follows :

A. 120/1 - 120/2 = 120 - 60 = 60 --> NO
B. 120/2 - 120/3 = 60 - 40 = 20 --> NO
C. 120/3 - 120/4 = 40 - 20 = 10 --> YES

The correct answer is C.
Anju Agarwal
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Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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by Anju@Gurome » Mon Apr 08, 2013 5:00 am
Algebraic Solution:
Let us assume that current price for each towel is $P.
Hence, in $120, 120/P towels can bought.

In new price of $(P + 1), 120/(P + 1) towels can be bought.

So, 120/P - 120/(P + 1) = 10
--> 12/P - 12/(P + 1) = 1
--> [12(P + 1) - 12P]/[P(P + 1)] = 1
--> 12/[P(P + 1)] = 1
--> P(P + 1) = 12
--> P² + P - 12 = 0
--> P² + 4P - 3P - 12 = 0
--> P(P + 4) - 3(P + 4) = 0
--> (P - 3)(P + 4) = 0
--> Either P = 3 or P = -4

As price of towel cannot be negative, P = 3

The correct answer is C.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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by Brent@GMATPrepNow » Mon Apr 08, 2013 5:32 am
As Anju has shown, plugging in the answer choices is a great/fast approach.

Whenever you encounter a word problem, you should always consider the option of plugging in the answer choices as this may be the fastest approach. Unfortunately, a lot of students don't consider this strategy or they deem it to be a "novice" approach. Presumably, this opinion is a result of math teachers who insist on long, algebraic approaches in which students must show all of their work.

However, on the GMAT, our goal is not to please our former math teachers. Our goal is to identify the correct answer in as little time as possible.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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