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

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Senior Manager
Status: D-Day is on February 10th. and I am not stressed
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Location: Kuwait
Schools: Columbia university
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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25% (medium)

Question Stats:

66% (01:59) correct 34% (00:53) wrong based on 316 sessions

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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
[Reveal] Spoiler: OA

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Re: a company decreased the price [#permalink]

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19 Nov 2011, 12:33
1
KUDOS
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%

=> The required ratio = 100%/50% = 2.0

Option (D)
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Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: A company decreased the price of its main product by 50% [#permalink]

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26 Mar 2012, 01:17
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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

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). Hence the ratio is 100%/50%=2. Answer: D. _________________ Math Expert Joined: 02 Sep 2009 Posts: 39662 Re: A company decreased the price of its main product by 50% [#permalink] ### Show Tags 18 Nov 2013, 06:57 1 This post received KUDOS Expert's post 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. This is my reasoning with number: Initial price= 100 Initial Units=100 x=new quantity (100)(100)=10,000 (.5)(100)(x)=10,000 x=200 (new quantity) Quantity percent increase= (200-100/100)(100)=100% increase Price decrease= (100-50/50)=100% decrease 100/100=1 I know this is wrong, but can someone please help me understand why? Is the price decrease from 100 to 50 a 100% decrease? It's 50% decrease: (100-50)/100=0.5. Hope it's clear. _________________ Senior Manager Status: D-Day is on February 10th. and I am not stressed Affiliations: American Management association, American Association of financial accountants Joined: 12 Apr 2011 Posts: 263 Location: Kuwait Schools: Columbia university Re: a company decreased the price [#permalink] ### Show Tags 19 Nov 2011, 14:37 Thank you good and easy one. for some reason i couldn't solve it, maybe i was stressed while taking the test. thanks again _________________ Sky is the limit Manager Joined: 27 Oct 2011 Posts: 186 Location: United States Concentration: Finance, Strategy GPA: 3.7 WE: Account Management (Consumer Products) Re: a company decreased the price [#permalink] ### Show Tags 25 Mar 2012, 18:23 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 _________________ DETERMINED TO BREAK 700!!! Manager Joined: 12 Mar 2012 Posts: 93 Location: India Concentration: Technology, Strategy GMAT 1: 710 Q49 V36 GPA: 3.2 WE: Information Technology (Computer Software) Re: A company decreased the price of its main product by 50% [#permalink] ### Show Tags 26 Mar 2012, 01:22 In such questions it is always easier to chose random values and solve the question. Intern Joined: 21 Oct 2012 Posts: 25 GMAT Date: 01-19-2013 Re: A company decreased the price of its main product by 50% [#permalink] ### Show Tags 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. _________________ MGMAT1 - 610 MGMAT2 - 670 MGMAT3 - 640 OMG Intern Joined: 14 Sep 2013 Posts: 2 Re: A company decreased the price of its main product by 50% [#permalink] ### Show Tags 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. This is my reasoning with number: Initial price= 100 Initial Units=100 x=new quantity (100)(100)=10,000 (.5)(100)(x)=10,000 x=200 (new quantity) Quantity percent increase= (200-100/100)(100)=100% increase Price decrease= (100-50/50)=100% decrease 100/100=1 I know this is wrong, but can someone please help me understand why? Intern Joined: 14 Sep 2013 Posts: 2 Re: A company decreased the price of its main product by 50% [#permalink] ### Show Tags 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. This is my reasoning with number: Initial price= 100 Initial Units=100 x=new quantity (100)(100)=10,000 (.5)(100)(x)=10,000 x=200 (new quantity) Quantity percent increase= (200-100/100)(100)=100% increase Price decrease= (100-50/50)=100% decrease 100/100=1 I know this is wrong, but can someone please help me understand why? Is the price decrease from 100 to 50 a 100% decrease? It's 50% decrease: (100-50)/100=0.5. Hope it's clear. yes it is. I made a very silly mistake. Thank you so much for clarifying! Current Student Joined: 21 Oct 2013 Posts: 193 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Re: A company decreased the price of its main product by 50% [#permalink] ### Show Tags 02 Jun 2014, 23:44 I also used an algebraic approach: initial revenue: p * u = r (p = price; u = units; r= revenue) now we have a decrease of 0.5 in p and an increase of x in u. r remains the same: 0.5p * (x*u) = r now equalize: 0.5p * (x*u) = p * u ==> p/0.5p = x*u/u ==> 0.5p=x ==> x = 2 --> here's our ratio! dunno if this it the right approach but it worked for me lol. Intern Joined: 12 Apr 2013 Posts: 37 Concentration: Entrepreneurship, Strategy A company decreased the price of its main product by 50% [#permalink] ### Show Tags 11 Aug 2015, 04:35 1 This post was BOOKMARKED Revenue = Price of product * Units sold Old -$1000 = $100 * 10 New -$1000 = \$50 * 20

Percent decrease of price of product = (100 - 50)/100 *100 = 50

Percent increase of units sold = (20 - 10)/10 *100 = 100

Required ratio = 100/50 = 2 (Answer choice D)
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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).
Re: A company decreased the price of its main product by 50%   [#permalink] 21 May 2017, 17:44
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# A company decreased the price of its main product by 50%

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