GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 May 2018, 10:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# D01-26

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45248

### Show Tags

16 Sep 2014, 00:12
3
KUDOS
Expert's post
20
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

46% (02:18) correct 54% (02:35) wrong based on 178 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: 45248 Re D01-26 [#permalink] ### Show Tags 16 Sep 2014, 00:12 3 This post received KUDOS Expert's post 6 This post was BOOKMARKED 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 $$\frac{144}{16}-\frac{144}{18}=9-8=1$$.

_________________
Intern
Joined: 08 Aug 2014
Posts: 8

### Show Tags

29 Dec 2014, 11:59
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.
Current Student
Joined: 12 Aug 2015
Posts: 4
Schools: Wharton '18 (A)
GMAT 1: 710 Q50 V36

### Show Tags

14 Sep 2015, 10:26
2
KUDOS
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.
Current Student
Joined: 12 Aug 2015
Posts: 291
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

### Show Tags

14 Sep 2015, 11:05
3
KUDOS
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
_________________

KUDO me plenty

Manager
Joined: 05 Jul 2015
Posts: 105
GMAT 1: 600 Q33 V40
GPA: 3.3

### Show Tags

17 Feb 2016, 13:38
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: 60 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, 18:19 "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: 84 Location: United States WE: Engineering (Transportation) Re D01-26 [#permalink] ### Show Tags 29 Nov 2016, 04:33 I think this is a high-quality question. Intern Joined: 10 Dec 2016 Posts: 24 Re: D01-26 [#permalink] ### Show Tags 26 Dec 2016, 01:40 high Quality ! Intern Joined: 15 Jan 2017 Posts: 1 Re: D01-26 [#permalink] ### Show Tags 16 Jan 2017, 16:31 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: 14 Location: United States (NY) Concentration: Sustainability GPA: 3.76 WE: Other (Military & Defense) Re D01-26 [#permalink] ### Show Tags 25 Jul 2017, 19:29 1 This post received KUDOS 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 Intern Joined: 09 Jun 2014 Posts: 20 Location: United States Concentration: General Management, Operations Re: D01-26 [#permalink] ### Show Tags 18 Dec 2017, 07:07 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
Intern
Joined: 20 Jun 2017
Posts: 35
GMAT 1: 580 Q36 V32
GMAT 2: 660 Q39 V41
GRE 1: 319 Q159 V160

### Show Tags

24 Jan 2018, 18:08
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: 45248 Re: D01-26 [#permalink] ### Show Tags 24 Jan 2018, 21:13 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.
_________________
Re: D01-26   [#permalink] 24 Jan 2018, 21:13
Display posts from previous: Sort by

# D01-26

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.