Hard PS

[jsasipriya]

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

OA E

I find it difficult to form equation. Can someone guide me here?

Thanks!

[Anurag@Gurome]

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

Say the cook bought x eggs and paid $12.
Therefore price per dozen in dollar = 12*(12/x) = (144/x)

Now 2 extra eggs are added but the price remains same.
Therefore price per dozen in dollar = 12*(12/(x+2)) = (144/(x + 2))
According to the question, this price is $1 less than the previous price.

Hence the equation is:

• (144/x) - 1 = (144/(x + 2))

Now we have to find (x + 2).
Therefore, we can solve this quadratic for x or plug the answer choices for (x + 2).

Plugging the answer choices, only option E works.

The correct answer is E.

[GMATGuruNY]

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

OA E

I find it difficult to form equation. Can someone guide me here?

Thanks!

Rather than set up a messy equation, we can plug in the answer choices, which represent the number of eggs brought home. When 2 fewer eggs are purchased, the price for 12 eggs must decrease by 100 cents. Thus, when 2 fewer eggs are purchased, the difference in the cost per egg must be 100/12 = 8.33 cents per egg.

Answer choice C: 15 eggs brought home
1200/15 = 80 cents per egg.
1200/13 = 92.03 cents per egg.
Difference = 92.03 - 80 = 12.03.
Too big. Need to bring home more eggs.

Answer choice D: 16 eggs brought home
1200/16 = 75 cents per egg.
1200/14 = 85.71 cents per egg.
Difference = 85.71 - 75 = 10.71.
Too big. Need to bring home more eggs.

The correct answer is E.

Answer choice E: 18 eggs brought home
1200/18 = 66.67 cents per egg.
1200/16 = 75 cents per egg.
Difference = 75 - 66.67 = 8.33 cents per egg. Success!