GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 00:10 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  D01-26

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58335

Show Tags

3
30 00:00

Difficulty:   95% (hard)

Question Stats: 46% (02:20) correct 54% (03:04) wrong based on 144 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 V Joined: 02 Sep 2009 Posts: 58335 Re D01-26 [#permalink] Show Tags 3 7 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: 7

Show Tags

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.
Intern  Joined: 12 Aug 2015
Posts: 3
Schools: Wharton '18 (A)
GMAT 1: 710 Q50 V36 Show Tags

4
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.
Senior Manager  Joined: 12 Aug 2015
Posts: 280
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

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
_________________
KUDO me plenty
Manager  Joined: 05 Jul 2015
Posts: 94
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40 GPA: 3.3

Show Tags

1
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: 55 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 "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: 77 Location: United States WE: Engineering (Transportation) Re D01-26 [#permalink] Show Tags I think this is a high-quality question. Intern  B Joined: 10 Dec 2016 Posts: 23 Re: D01-26 [#permalink] Show Tags high Quality ! Intern  Joined: 15 Jan 2017 Posts: 1 Re: D01-26 [#permalink] Show Tags 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  B 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 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 Senior Manager  P Joined: 09 Jun 2014 Posts: 352 Location: India Concentration: General Management, Operations Re: D01-26 [#permalink] Show Tags 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  B
Joined: 20 Jun 2017
Posts: 32
GMAT 1: 580 Q36 V32 GMAT 2: 660 Q39 V41 GRE 1: Q159 V160 Show Tags

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 V Joined: 02 Sep 2009 Posts: 58335 Re: D01-26 [#permalink] Show Tags 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 $$\frac{144}{16}-\frac{144}{18}=9-8=1$$.

Can you solve the quadratic?

Yes but it's much better to substitute the options because you are getting ugly quadratics: x^2 + 2x - 288 = 0.
_________________
Intern  B
Joined: 09 Jan 2018
Posts: 21
Location: Australia
Schools: Booth '21 (II)
GRE 1: Q164 V162 GRE 2: Q164 V162 GPA: 3.63

Show Tags

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
Intern  S
Joined: 16 Aug 2014
Posts: 49

Show Tags

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.
_________________
Hit Kudos if you like the post
Director  P
Joined: 20 Sep 2016
Posts: 633
Location: India
Concentration: Strategy, Operations
GPA: 3.95
WE: Operations (Real Estate)

Show Tags

@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
Manager  B
Joined: 07 Apr 2018
Posts: 101
Location: United States
Concentration: General Management, Marketing
GMAT 1: 600 Q45 V28 GPA: 3.8

Show Tags

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
Intern  B
Joined: 06 Dec 2016
Posts: 1

Show Tags

When you get the answer - do not just jump to the option and tick the answer.
Before selecting the option - CHECK ALWAYYYYYSSSSS - What is the questn asking for - (How many eggs he took HOME) not
How many eggs are there, i.e 16. The answer is - 16+2 = 18 (as he asked for 2 more eggs)
Intern  B
Joined: 26 Dec 2018
Posts: 7

Show Tags

How can I tell the source of a question? Like I want to know if this question came from a 3rd party company, an OG book, or a question someone just decided the make up.

If this is an OG question, can I assume that all the questions tested in the GMAT CATs are OG? Re: D01-26   [#permalink] 17 Jul 2019, 15:05

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by

D01-26

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  