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A company decreased the price of its main product by 50% [#permalink]

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19 Nov 2011, 12:14

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A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?

For the total revenue to remain the same when the price is halved, the number of products sold must double. Therefore increase in the number of products sold is 100%

Price decreased so quantity must increase so the net effect of the 50% decrease and % increase in quantity must equal 1. And that is 200% increase. We are looking for the net % increase which is 100% increase and then take the ratio of that which is 100%/50% = 2. D
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A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?

A. 0.5 B. 1.0 C. 1.5 D. 2.0 E. 4.0

Nice explanation above by GyanOne.

One can also use plug-in method: consider the price of the product to be $10 and the units sold at that price to be 1 --> revenue=$10*1=$10;

If we decrease the price by 50% from $10 to $5 then in order the revenue to remain the same 2 units must be sold which is 100% increase in sales (from 1 to 2).

Re: A company decreased the price of its main product by 50% [#permalink]

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30 Dec 2012, 17:56

I used algebraical approach: 1) p1=p2 We know that p1q1=p2q2, let's apply here condition (1) ===> 2p2q1=p2q2. It means that 2q1=q2 or q2/q1=2 Manhattan CAT2 consider this question 700-800 which is not true.
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Re: A company decreased the price of its main product by 50% [#permalink]

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18 Nov 2013, 06:53

I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

Re: A company decreased the price of its main product by 50% [#permalink]

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18 Nov 2013, 13:14

Bunuel wrote:

sarahmichalmoore wrote:

I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

Re: A company decreased the price of its main product by 50% [#permalink]

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01 Oct 2016, 04:50

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Re: A company decreased the price of its main product by 50% [#permalink]

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21 May 2017, 17:44

manalq8 wrote:

A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?

A. 0.5 B. 1.0 C. 1.5 D. 2.0 E. 4.0

Smart numbers are the best solution to this problem.

If we start with PQ =4 and P =2 and Q =2, then we know that P becomes 1 and Q becomes 4. 4/2 = 1 = 100% growth for Q whereas we know that P decreased by 50%.

100%/50% = 2.0 or 200%, the ratio of the increase in quantity to the decrease in price (elasticity of the good).

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