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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

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by coolhabhi » Wed May 06, 2015 5:53 am
[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]

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by GMATGuruNY » Wed May 06, 2015 5:54 am
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
To determine the revenue ratio for 1986 to 1985, TEST AN EASY CASE.

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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by j_shreyans » Wed May 06, 2015 9:07 am
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.

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by [email protected] » Wed May 06, 2015 9:15 am
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

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by Scott@TargetTestPrep » Wed Jan 03, 2018 4:05 pm
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
We can let the number of pairs of shoes sold in 1985 = n and the price per pair = p.

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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