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
Use backsolving
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pullagurla
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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?
Algebraic Approach
X ---- N towels => XN = 120 or X = 120/N
X+1 ------ N - 10 towels =>
(X+1) * (N-10) = 120
XN - 10X + N - 10 =120.
Substituting the value of X
120 - 1200/N + N - 10 = 120
-1200/N +N = 10
-1200 + N^2 = 10N
N^2 - 10N - 1200 = 0
(10 + 70 )/2 or (10 - 70)/2
We can reject the negative value
So .. N = 40
XN = 120
N = 40
X = 3 - our answer.
X - 1 = new price
So answer is C - 3 dollars
Back Solving approach
A - If current price is 1 dollars, So we can buy 120 towels now, if it were 2 dollars we would have been able to buy 60 towels, Difference between number of towels that can bought should be 10. In this case its 60 so ruled out
B - Current price is 2 dollars so we can buy 60 towels, if it were 3 dollars we could have bought 40 towels, Difference = 20, reject.
C - Current price 3 so we can buy 40 towels, it were 4, we could have bought 30 towels, difference = 10 and hence this is our answer.
Hence answer is C
(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
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?
Algebraic Approach
X ---- N towels => XN = 120 or X = 120/N
X+1 ------ N - 10 towels =>
(X+1) * (N-10) = 120
XN - 10X + N - 10 =120.
Substituting the value of X
120 - 1200/N + N - 10 = 120
-1200/N +N = 10
-1200 + N^2 = 10N
N^2 - 10N - 1200 = 0
(10 + 70 )/2 or (10 - 70)/2
We can reject the negative value
So .. N = 40
XN = 120
N = 40
X = 3 - our answer.
X - 1 = new price
So answer is C - 3 dollars
Back Solving approach
A - If current price is 1 dollars, So we can buy 120 towels now, if it were 2 dollars we would have been able to buy 60 towels, Difference between number of towels that can bought should be 10. In this case its 60 so ruled out
B - Current price is 2 dollars so we can buy 60 towels, if it were 3 dollars we could have bought 40 towels, Difference = 20, reject.
C - Current price 3 so we can buy 40 towels, it were 4, we could have bought 30 towels, difference = 10 and hence this is our answer.
Hence answer is C
(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
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I love this question!pullagurla wrote: ↑Thu Sep 02, 2010 10:42 pmA 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
Use backsolving
It's a great example of the distinction between high school math and GMAT math.
High school math approach:
Start with the word equation: (number of towels purchased for $120 at CURRENT price) = (number of towels purchased for $120 at INCREASED price) + 10
Let x = the CURRENT price / towel (in dollars)
So, x+1 = the INCREASED price / towel (in dollars)
Plug these values into the word equation to get: 120/x = 120/(x+1) + 10
Multiply both sides of the equation by x to get: 120 = 120x/(x +1) + 10x
Multiply both sides of the equation by (x+1) to get: 120(x+1) = 120x + 10x(x+1)
Expand to get: 120x + 120 = 120x + 10x² + 10x
Subtract 120x from both sides: 120 = 10x² + 10x
Subtract 120 from both sides: 0 = 10x² + 10x - 120
Divide both sides by 10 to get: 0 = x² + x - 12
Factor: 0 = (x + 4)(x - 3)
So, EITHER x = -4 OR x = 3
Since the price of a towel cannot be negative, the correct answer is x = 3
Answer: C
GMAT math approach: Take advantage of the fact that it's super easy (and super fast) to test the answer choices for this question.
(A) $1. At this price, I can buy 120 towels. At the increased price of $2, I can buy 60 towels.
That’s 60 fewer towels. The question says 10 fewer towels. ELIMINATE A.
(B) $2. At this price, I get 60 towels. At $3 per towel, I get 40 towels.
That’s 20 fewer towels. ELIMINATE B.
(C) $3. This gets me 40 towels. $4 gets me 30 towels.
That’s 10 fewer towels. DONE!
Answer: C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
