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D01-26

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D01-26 [#permalink]

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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
[Reveal] Spoiler: OA

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Official Solution:

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 # of eggs the cook originally got was \(x\);

The price per egg then would be \(\frac{12}{x}\) and the price per dozen would be \(12*\frac{12}{x}\).

Now, since the cook talked the seller into adding two more eggs then he finally got \(x+2\) eggs (notice that \(x+2\) is exactly what we should find);

So, the price per egg became \(\frac{12}{x+2}\) and the price per dozen became \(12*\frac{12}{x+2}\).

As after this the price per dozen went down by a dollar then \(12*\frac{12}{x}-12*\frac{12}{x+2}=1\), which simplifies to \(\frac{144}{x}-\frac{144}{x+2}=1\). At this point it's better to substitute the values from answer choices rather than to solve for \(x\). Answer choices E fits: if \(x+2=18\) then \(\frac{144}{16}-\frac{144}{18}=9-8=1\).


Answer: E
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New post 29 Dec 2014, 10:59
Good question. Having both 16 and 18 as answer choices is a bit cruel though. I solved the quadratic for x and got 16. I forgot that the question asked as to determine x+2. If 16 weren't there as a possible answer choice I would have realized what the question was asking.

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Re: D01-26 [#permalink]

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Need to be able to confidently represent 'price per unit', and answering this question correctly requires such.

memo: price per unit is total price / total quantity; as such, 'price per egg' can be represented as '12 / x', where x = the unknown quantity of eggs. The next step is recognizing that '12 / x' is a generic statement for the price of each egg; hence, 12 * (12/x) = the price per dozen eggs. The fact that the numerator in '12/x' is 12 is a coincidence and should not cause confusion in your attempt to answer the question.

Thus, if given 2 new eggs for free (i.e. x + 2), then the new 'price per dozen' can be represented as '12 * (12 / x +2)'. We can set up an equality here to highlight the fact that this new equation yields a 'price per dozen eggs' (or 12 * 12/x) that is 1 less than the original equation; hence [12 * (12 / x+2)] = [12 * (12/x)] - 1

Solving for x will yield 16; thus, x + 2 = 18, which is the correct answer.

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Re: D01-26 [#permalink]

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a 30 sec solution: think like a test-maker

the testmaker want to trick and trap you right? mean testmaker always includes right answers but to different questions.

here you know that the difference should be 2. hence the whole thing smells like an alegbraic manipulation. when doing algebra people do everything right but forget to look back at what the questions asks. testmaker exploits this.

so we have 2 contenders for the right answer D and E as the difference between them is 2.

if the question asked how many egg did the seller initially give to the cook, the answer would be the lower number - D
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Re: D01-26 [#permalink]

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New post 17 Feb 2016, 12:38
I back-solved and looked for two numbers $1 apart.

Starting with C: He paid $12 for 15 eggs = (4/5) *12 = 9.60 Had he paid $12 for 13 eggs * 12 = 11.something. More than a dollar

E. He paid $12 for 8 eggs = (2/3)*12 = 8 Had he gotten 16... 12/16 = (3/4)*12 = 9
8 and 9 are $1 away. If E had been less than a dollar, answer would have been D.

Answer E.

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Re: D01-26 [#permalink]

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New post 24 Mar 2016, 17:19
"As the two eggs were added, the price per dozen went down by a dollar",
If you have 12 eggs, 2 of these eggs are free, and the normal price would be a dollar more, it can mean that each egg costs 0.5, and that the normal dozen would cost 6 dollars.
what part of the logic am I getting wrong?

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Re D01-26 [#permalink]

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New post 29 Nov 2016, 03:33
I think this is a high-quality question.

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Re: D01-26 [#permalink]

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New post 26 Dec 2016, 00:40
high Quality !

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Re: D01-26 [#permalink]

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New post 16 Jan 2017, 15:31
I was thrown off by the fact that it said "some of the eggs and paid for $12". I thought that meant an X amount for 12 dollars. Secondly, after looking at the solution, I can't get over the fact that someone will pay $12 for a egg. Supply must be very limited.

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Re D01-26 [#permalink]

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New post 25 Jul 2017, 18:29
I think this is a high-quality question and I agree with explanation. 18/12=3/2
16/12=4/3

3/2*4/4=12/8
4/3*3/3=12/9

9-8=1

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Re: D01-26 [#permalink]

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New post 18 Dec 2017, 06:07
Bunuel 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



My take:Using options and without algebra

The answer choices will have 2 extra added eggs..so lets take E
actual x =18-2=16

Now 12/16(*12)--(12/18)(*12)
9-8=1

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Re: D01-26   [#permalink] 18 Dec 2017, 06:07
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