OG2016- PS 208

Question

GMATGuruNY · Answer

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
We can let Q = quantity of towels sold and P = price per towel sold and create the equations:

PQ = 120

Q = 120/P

And

(P + 1)(Q – 10) = 120

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

120 – 10P + 120/P – 10 = 120

–10P + 120/P – 10 = 0

–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.

Alternate Solution:

Let’s test each answer choice.

A) If the price of a towel was $1, then 120/1 = 120 towels can be bought before the increase and 120/2 = 60 towels can be bought after the increase, which is 60 fewer. A is not correct.

B) If the price of a towel was $2, then 120/2 = 60 towels can be bought before the increase and 120/3 = 40 towels can be bought after the increase, which is 20 fewer. B is not correct.

A) If the price of a towel was $3, then 120/3 = 40 towels can be bought before the increase and 120/4 = 30 towels can be bought after the increase, which is 10 fewer. C is correct.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Brent@GMATPrepNow · Answer

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
We can let Q = quantity of towels sold and P = price per towel sold and create the equations:

PQ = 120

Q = 120/P

And

(P + 1)(Q – 10) = 120

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

120 – 10P + 120/P – 10 = 120

–10P + 120/P – 10 = 0

–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.

Alternate Solution:

Let’s test each answer choice.

A) If the price of a towel was $1, then 120/1 = 120 towels can be bought before the increase and 120/2 = 60 towels can be bought after the increase, which is 60 fewer. A is not correct.

B) If the price of a towel was $2, then 120/2 = 60 towels can be bought before the increase and 120/3 = 40 towels can be bought after the increase, which is 20 fewer. B is not correct.

A) If the price of a towel was $3, then 120/3 = 40 towels can be bought before the increase and 120/4 = 30 towels can be bought after the increase, which is 10 fewer. C is correct.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ceilidh.erickson · Answer

One common source of confusion on this question: the question doesn't explicitly state that current total cost is $120. Many students wonder how we're allowed to set the equation equal to that amount. But we are allowed to infer based on inverse proportionality (and common sense!). The relationship between price and quantity is always:
pq = total cost

If we want to keep the total cost constant, then when the price goes up, the quantity will go down, and vice versa. Any time you have a product of two variables equaling a constant, they will be inversely proportional: (wage)(hours)=income, etc.

In this problem, we're told that if price goes up by a certain amount, then the quantity would have to go down by a specified amount to equal $120. By saying "10 fewer of the towels could be bought for $120," it's implying "10 fewer than before, when the total was also $120."

All the experts here are in agreement: we would Work Backwards from the answer choices. Whenever a PS question asks for the value of an unknown (variable), one option is to plug the answer choices back into the problem to see which one works.

A slightly different spin on working backwards (rather than Mitch's strategy of going 1 answer choice at a time) is to set up a table.
Here are the answer choice options for p, and the corresponding value of q that would equal $120:
p x q
1 x 120
2 x 60
3 x 40
4 x 30
12 x 10

Now add 1 to each price and subtract 10 from each quantity:
p x q
1 x 120 --> 2 x 110 --> 220. no
2 x 60 --> 3 x 50 --> 150. no.
3 x 40 --> 4 x 30 --> 120. yes!
4 x 30 --> 5 x 20 --> 100. no.
12 x 10 --> 13 x 0 --> 0. no.

For which of these new pairs does pq = 120? Only 4 x 30. The answer must be C.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Rich.C@EMPOWERgmat.com · Answer

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: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Jeff@TargetTestPrep · Answer

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
We can let Q = quantity of towels sold and P = price per towel sold and create the equations:

PQ = 120

Q = 120/P

And

(P + 1)(Q – 10) = 120

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

120 – 10P + 120/P – 10 = 120

–10P + 120/P – 10 = 0

–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.

Alternate Solution:

Let’s test each answer choice.

A) If the price of a towel was $1, then 120/1 = 120 towels can be bought before the increase and 120/2 = 60 towels can be bought after the increase, which is 60 fewer. A is not correct.

B) If the price of a towel was $2, then 120/2 = 60 towels can be bought before the increase and 120/3 = 40 towels can be bought after the increase, which is 20 fewer. B is not correct.

A) If the price of a towel was $3, then 120/3 = 40 towels can be bought before the increase and 120/4 = 30 towels can be bought after the increase, which is 10 fewer. C is correct.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

OG2016- PS 208

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER