In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?
(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million
Please provide a detailed solution for this problem
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[quote="Architj"]In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?
(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million[/quote]
Suppose in the year 1985 the number of pairs of shoes sold = 100 &
the price per pair = 100 => the Total Revenue = 100x100 = 10000
Then in the year 1986 the number of pairs of shoes sold = 80 &
the price per pair = 120 => the Total Revenue = 80x120 = 9600
It is given the company's revenue from the sale of the shoes in 1986 was $3.0 million
So if 9600 equals $3.0 million
then 10000 equals = (10000/9600)x $3.0 million = 1.042 x $3.0 million = 3.125 million
Answer [spoiler]D[/spoiler]
(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million[/quote]
Suppose in the year 1985 the number of pairs of shoes sold = 100 &
the price per pair = 100 => the Total Revenue = 100x100 = 10000
Then in the year 1986 the number of pairs of shoes sold = 80 &
the price per pair = 120 => the Total Revenue = 80x120 = 9600
It is given the company's revenue from the sale of the shoes in 1986 was $3.0 million
So if 9600 equals $3.0 million
then 10000 equals = (10000/9600)x $3.0 million = 1.042 x $3.0 million = 3.125 million
Answer [spoiler]D[/spoiler]
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To determine the revenue ratio for 1986 to 1985, TEST AN EASY CASE.Architj wrote:In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?
(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million
1985:
Let the number of pairs sold = 10.
Let the price per pair = 10.
Total revenue = (number of pairs)(price per pair) = 10*10 = 100.
1986:
Since 20% fewer pairs are sold, the number of pairs = 10 - 20% of 10 = 10-2 = 8.
Since the price per pair increases by 20%, the price per pair = 10 + 20% of 10 = 10+2 = 12.
Total revenue = (number of pairs)(price per pair) = 8*12 = 96.
Resulting ratio:
(revenue in 1986)/(revenue in 1985) = 96/100 = 24/25.
Since the actual revenue in 1986 = 3 million, set up the following proportion:
24/25 = 3/x
24x = 75
x = 3.125.
The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
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Hi ,
Can you please advise that why did you do by taking ratio? Is there any other method to solve this?
Resulting ratio:
(revenue in 1986)/(revenue in 1985) = 96/100 = 24/25.
Since the actual revenue in 1986 = 3 million, set up the following proportion:
24/25 = 3/x
24x = 75
x = 3.125.
Can you please advise that why did you do by taking ratio? Is there any other method to solve this?
Resulting ratio:
(revenue in 1986)/(revenue in 1985) = 96/100 = 24/25.
Since the actual revenue in 1986 = 3 million, set up the following proportion:
24/25 = 3/x
24x = 75
x = 3.125.
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Hi All,
This question can be dealt with in a number of different ways. Here's an algebraic approach:
N = number of pairs of shoes
P = price per pair
1985 = (N)(P)
We're then told that in 1986 the NUMBER of pairs DECREASED by 20% and the PRICE per pair INCREASED by 20%....
1986 = (.8N)(1.2P) = .96(N)(P)
We're then told that revenue in 1986 was $3.0 million....
.96NP = 3,000,000
And we're asked for the revenue in 1985, which means that we want the value of (N)(P)...
NP = 3,000,000/.96
From this, we can see the NP is a little greater than 3,000,000. There's only one answer that fits...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question can be dealt with in a number of different ways. Here's an algebraic approach:
N = number of pairs of shoes
P = price per pair
1985 = (N)(P)
We're then told that in 1986 the NUMBER of pairs DECREASED by 20% and the PRICE per pair INCREASED by 20%....
1986 = (.8N)(1.2P) = .96(N)(P)
We're then told that revenue in 1986 was $3.0 million....
.96NP = 3,000,000
And we're asked for the revenue in 1985, which means that we want the value of (N)(P)...
NP = 3,000,000/.96
From this, we can see the NP is a little greater than 3,000,000. There's only one answer that fits...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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We can let the number of pairs of shoes sold in 1985 = n and the price per pair = p.Architj wrote:In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?
(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million
Thus, the revenue in 1985 is np and we can create the following equation for the revenue in 1986:
(0.8n)(1.2p) = 3,000,000
0.96np = 3,000,000
np = 3,125,000, which is roughly 3.1 million.
Answer: D
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