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A cook went to a market to buy some eggs and paid $12. But s

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by varun289 » Sat Apr 13, 2013 10:41 am
A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?

A. 8
B. 12
C. 15
D. 16
E. 18








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by Anju@Gurome » Sat Apr 13, 2013 10:53 am
varun289 wrote:A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?
Let's assume initially he bought n eggs.
So, price per dozen = $(12*12/n)

But finally he bought (n + 2) eggs for $12.
So, price per dozen = $(12*12/(n + 2))

So, 12*12/n - 12*12/(n + 2) = 1
--> (12*12)[(n + 2) - n]/[n(n + 2)] = 1
--> 144*2 = n(n + 2)
--> n(n + 2) = 288

Now, we can either solve the above quadratic equation as follows,
  • --> n² + 2n - 288 = 0
    --> n² + 18n - 16n - 288 = 0
    --> (n + 18)(n - 16) = 0
    --> As n must be positive, n = 16
Or we can plug (answer choice - 2) to see which of them satisfy the equation.

Hence, he bought (16 + 2) = 18 eggs.

The correct answer is E.
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by GMATGuruNY » Sat Apr 13, 2013 2:46 pm
varun289 wrote:A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?

A. 8
B. 12
C. 15
D. 16
E. 18
After two eggs are added, the price per DOZEN decreases by $1.
Thus, the price per EGG decreases by 1/12 of a dollar.
We can plug in the answers, which represent the number of eggs taken home.

The answer choices imply the following options for the price per egg AFTER two eggs are added:
12/8 = 3/2
12/12 = 1
12/15 = 4/5
12/16 = 3/4
12/18 = 2/3.

BEFORE two eggs are added, the price per egg must be one of the following options:
12/6 = 2
12/10 = 6/5
12/13
12/14 = 6/7
12/16 = 3/4.

Since the difference between the two prices must be 1/12, look for an answer choice that yields two denominators whose product is a multiple of 12.
Only E works:
3/4 - 2/3 = 1/12.
Success!

The correct answer is E.
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