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units sold after the reduction

by sanju09 » Mon Apr 18, 2011 12:49 am
In order to increase its revenue a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its revenue. What is the percent increase in the number of units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up
Last edited by sanju09 on Mon Apr 18, 2011 2:19 am, edited 1 time in total.
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by manpsingh87 » Mon Apr 18, 2011 1:37 am
sanju09 wrote:In order to increase its sales a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its sales. What is the percent increase in the units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up
let the price of the unit be x, and sales be y, No. of units sold=y/x;
after reduction price of the unit=.8x and sales becomes 1.28y, No. of units sold=1.28y/.8x;

hence percent increase in the unit sold={(1.28y/.8x-y/x)/(y/x)}*100;
(128/80-1)*100; 48/80*100=60% hence D
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by Stuart@KaplanGMAT » Mon Apr 18, 2011 2:09 am
Hi,

I think there's a mistake in the question, since the stem clearly states that there's a 28% increase in sales (a term which usually refers to the number of units sold). Did you mean to say that there's a 28% increase in gross revenue?

Alternatively, if that part of the question is correct, then the final sentence needs to be changed to "what is the percent increase in revenue after the reduction?".

As it stands, the common interpretation would be that there's a 28% increase in the number of units sold, which clearly isn't what you intended.
sanju09 wrote:In order to increase its sales a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its sales. What is the percent increase in the units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up
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by sanju09 » Mon Apr 18, 2011 2:16 am
Stuart Kovinsky wrote:Hi,

I think there's a mistake in the question, since the stem clearly states that there's a 28% increase in sales (a term which usually refers to the number of units sold). Did you mean to say that there's a 28% increase in gross revenue?

Alternatively, if that part of the question is correct, then the final sentence needs to be changed to "what is the percent increase in revenue after the reduction?".

As it stands, the common interpretation would be that there's a 28% increase in the number of units sold, which clearly isn't what you intended.
sanju09 wrote:In order to increase its revenue a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its revenue. What is the percent increase in the units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up
Mistake admitted and edited, thanks
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by sanju09 » Mon Apr 18, 2011 3:20 am
manpsingh87 wrote:
sanju09 wrote:In order to increase its revenue a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its revenue. What is the percent increase in the number of units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up
let the price of the unit be x, and sales be y, No. of units sold=y/x;
after reduction price of the unit=.8x and sales becomes 1.28y, No. of units sold=1.28y/.8x;

hence percent increase in the unit sold={(1.28y/.8x-y/x)/(y/x)}*100;
(128/80-1)*100; 48/80*100=60% hence D

Always avoid using more than necessary variables to save time and calculation intricacies.

If initially 100 was the price of each unit and 100 happened to be the number of units sold, then 100 × 100 = 10,000 was the revenue.

Now, if the price of each unit becomes 80 and it results in an increase of x percent in the number of units sold after the reduction, then according to the question the revenue becomes 28 percent more than 10,000, mathematically

80 (100 + x) = 12,800

80 x = 4,800 or x = [spoiler]60%


D[/spoiler]
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