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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
A store currently charges the same price for each towel that
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08 Sep 2020, 07:32
08 Sep 2020, 07:32
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44% (00:46) correct
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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?
(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
Source: GMAT Official Guide
(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
Source: GMAT Official Guide
Re: A store currently charges the same price for each towel that
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08 Sep 2020, 10:30
08 Sep 2020, 10:30
1
Quote:
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?
Step 1: Understanding the question
Let initial price and number of towel be p and n respectively
Total initial price is p*n = 120 ---- (I)
New price and number of towels are (p+1) and (n-10)
Hence, new total price is (p+1)*(n-10) = 120 ----- (II)
Step 2: Calculation
Using the options and substituting value of p in equation (II)
A. When p=1; 2*(n-10) = 120 => n = 70; as p*n is not equal to 120, eliminate
B. When p=2; 3*(n-10) = 120 => n = 50; as p*n is not equal to 120, eliminate
C. When p=3; 4*(n-10) = 120 => n = 40; as p*n is equal to 120, Correct
C is correct
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
A store currently charges the same price for each towel that
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08 Sep 2020, 11:53
08 Sep 2020, 11:53
GreenlightTestPrep 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
Source: GMAT Official Guide
(A) $ 1
(B) $ 2
(C) $ 3
(D) $ 4
(E) $12
Source: GMAT Official Guide
I love this question!
It's a great example of the distinction between high school math and GRE 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
GRE 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
