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# D01-26

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Math Expert
Joined: 02 Sep 2009
Posts: 51167

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15 Sep 2014, 23:12
3
23
00:00

Difficulty:

95% (hard)

Question Stats:

47% (02:09) correct 53% (02:30) wrong based on 221 sessions

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 _________________ Math Expert Joined: 02 Sep 2009 Posts: 51167 Re D01-26 [#permalink] ### Show Tags 15 Sep 2014, 23:12 3 6 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 $$\frac{144}{16}-\frac{144}{18}=9-8=1$$.

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Joined: 08 Aug 2014
Posts: 8

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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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Joined: 12 Aug 2015
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14 Sep 2015, 09:26
3
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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14 Sep 2015, 10:05
5
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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Joined: 05 Jul 2015
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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. Current Student Joined: 12 Nov 2015 Posts: 59 Location: Uruguay Concentration: General Management Schools: Goizueta '19 (A) GMAT 1: 610 Q41 V32 GMAT 2: 620 Q45 V31 GMAT 3: 640 Q46 V32 GPA: 3.97 Re: D01-26 [#permalink] ### Show Tags 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? Manager Joined: 05 Jun 2015 Posts: 82 Location: United States WE: Engineering (Transportation) Re D01-26 [#permalink] ### Show Tags 29 Nov 2016, 03:33 I think this is a high-quality question. Intern Joined: 10 Dec 2016 Posts: 24 Re: D01-26 [#permalink] ### Show Tags 26 Dec 2016, 00:40 high Quality ! Intern Joined: 15 Jan 2017 Posts: 1 Re: D01-26 [#permalink] ### Show Tags 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. Intern Joined: 17 Dec 2016 Posts: 13 Location: United States (NY) Concentration: Sustainability GPA: 3.76 WE: Other (Military & Defense) Re D01-26 [#permalink] ### Show Tags 25 Jul 2017, 18:29 1 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 Manager Joined: 09 Jun 2014 Posts: 218 Location: India Concentration: General Management, Operations Schools: Tuck '19 Re: D01-26 [#permalink] ### Show Tags 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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24 Jan 2018, 17:08
Bunuel wrote:
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 Can you solve the quadratic? Math Expert Joined: 02 Sep 2009 Posts: 51167 Re: D01-26 [#permalink] ### Show Tags 24 Jan 2018, 20:13 Mco100 wrote: Bunuel wrote: 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 $$\frac{144}{16}-\frac{144}{18}=9-8=1$$.

Yes but it's much better to substitute the options because you are getting ugly quadratics: x^2 + 2x - 288 = 0.
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Joined: 09 Jan 2018
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06 Jun 2018, 03:12
I think this is a high-quality question and I agree with explanation. very good question ! easy to fall in the trap of forgetting to add 2 to the final result
Manager
Joined: 16 Aug 2014
Posts: 54

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24 Sep 2018, 21:56
Hi Bunuel I solved this question in 3:17 min by plugging in Values for each option and finally stuck with choices D and E and select choice E.
Is there any other way to solve this question in 2 min except the one you explained.
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Joined: 20 Sep 2016
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24 Oct 2018, 05:24
@Bunuek

the price 12$was paid for x+2 items .. so price per item = 12/x+2 ..... my question = how did u consider the price for original items is 12$.... as per the Q , that price is paid for (original+2)..... please explain ... i dont understand how did u consider this : 12/x
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Joined: 07 Apr 2018
Posts: 72
Location: United States
Concentration: General Management, Marketing
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28 Oct 2018, 10:14
suppose price of 12 eggs was X
now price of 12 eggs is X-1

In 12 \$ earlier he would have got 12/( 12/x) eggs
now he will get 12/(12/(X-1)) Eggs
so 12/(12/(X-1)) - 12/( 12/x) =2;
X(X-1)=72

X=9;
Hence 12/(12/(X-1)) = 18
Re: D01-26 &nbs [#permalink] 28 Oct 2018, 10:14
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# D01-26

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