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# GMAT Diagnostic Test Question 26

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Re: GMAT Diagnostic Test Question 27 [#permalink]  04 Jan 2010, 20:57
djxilo wrote:
my approach:

Worked backwards plugging in answer choices. We basically need to find the answer choice that gets us a saving of $1.00/12 eggs (~8 cents savings per egg) If we plug-in answer choice E, we get a total price paid per egg of$0.67. Subtracting two eggs for the same purchase price of $12 implies an original price of$0.75 per egg.

$0.75 -$0.66 = ~8 cents in savings.

This is a good approach, solving it the other direction.
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Re: GMAT Diagnostic Test Question 27 [#permalink]  10 Jan 2010, 23:21
marcos4 wrote:
Quote:
suppose before added two more eggs, the price per dozen is X and there are Y dozen
so we have XY=12
and (X-1)(Y+1/6)=12

from above we can get Y=16/12, there are 16 eggs.
in the end, the cook brings 16+2=18 eggs home.

Hello,
I feel that flyingbunny's way is the simplest but there's one part I don't get it.

Quote:
we have XY=12

OK

Quote:
(X-1)

means in regular english "the price per dozen was reduced by 1$" Quote: (X-1)(Y+1/6)=12 Where does this 1/6 comes from ? Thanks ! 1/6 came from the 2 free eggs. 12 * 1/6 = 2. _________________ He who industriously sows and reaps is a good laborer, and worthy of his hire. But he who sows that which will be reaped by others, by those who will know not of and care not for the sower, is a laborer of a nobler order, and worthy of a more excellent reward. Albert Pike Thank you all for this club ! Manager Joined: 27 Jul 2010 Posts: 197 Location: Prague Schools: University of Economics Prague Followers: 1 Kudos [?]: 27 [0], given: 15 Re: GMAT Diagnostic Test Question 27 [#permalink] 09 Oct 2010, 06:54 defoue wrote: Target760 wrote: here is my solution: let's say no of eggs purchased = E price per dozen of eggs in first case = ($12/E)*12 i.e. price per egg multiply by 12, to get price per dozen
new price per dozen = ($12/[E+2])*12 now, the equation is; (old price per dozen) - (new price per dozen) = 1 i.e. {($12/E)*12} - {($12/[E+2])*12} = 1 solve for E, 144/E - 144/(E+2) = 1 144E + 288 - 144E = E(E+2) 288=E^2 +2E E^2 + 2E - 288 = 0 By factoring we get E^2 + 18E - 16E -288 = 0 E(E+18)-16(E+18)=0 (E+18)(E-16)=0 E= - 18, or 16 rejecting negative value we get E=16 (the original no of eggs purchased) no. of eggs brought home = E+2 or 16 + 2 = 18 Therefore, answer is E Hey man, could you pls explain how did you come to your factorization. I do not get the way you're going from : E^2 + 2E - 288 = 0 to E(E+18)-16(E+18)=0 Thx very much You can alway solve through discriminant, but it takes you to 4 + 288*4 = 289*4 =1156 - which makes a bit problem if you dont know the square root of 1156. My approach: - as we have -288 one root of the equation must be negative and one positive - as we have 2E, the yE and xE must sum in 2E ( y+x = 2 - the positive must be greater by 2 in absolute value) now: 288 is pretty close to 289 which is 17^2. Try 17+1 and 17-1 which makes 16*18 -> now 16 must be negative. then: (x-16)*(x+18) = 0 _________________ You want somethin', go get it. Period! Intern Joined: 25 Oct 2010 Posts: 18 Followers: 0 Kudos [?]: 2 [0], given: 1 Re: GMAT Diagnostic Test Question 27 [#permalink] 02 Nov 2010, 20:10 I used the same approach..and got my answer.This is a little tricky and took me just about 2 mins..the point is you need to be a little quick on quadratic equations in the calculation part.Nevertheless a good one. let's say no of eggs purchased = E price per dozen of eggs in first case = ($12/E)*12 i.e. price per egg multiply by 12, to get price per dozen
new price per dozen = ($12/[E+2])*12 now, the equation is; (old price per dozen) - (new price per dozen) = 1 i.e. {($12/E)*12} - {($12/[E+2])*12} = 1 solve for E, 144/E - 144/(E+2) = 1 144E + 288 - 144E = E(E+2) 288=E^2 +2E E^2 + 2E - 288 = 0 By factoring we get E^2 + 18E - 16E -288 = 0 E(E+18)-16(E+18)=0 (E+18)(E-16)=0 E= - 18, or 16 rejecting negative value we get E=16 (the original no of eggs purchased) no. of eggs brought home = E+2 or 16 + 2 = 18 Therefore, answer is E Intern Status: Who Dares Wins -SAS Joined: 17 May 2010 Posts: 31 Schools: NYU, Ross, GSB Chicago, Darden, Tuck Followers: 0 Kudos [?]: 3 [0], given: 16 Re: GMAT Diagnostic Test Question 27 [#permalink] 05 Jan 2011, 08:38 The way I did it: Let the total number of eggs bought originally be x, setting up the eqn 12*(12/x - 12/(x+2))=1 ............... I Now during the test I used the brute force method where I solved the eqn and then tried to use the quadratic formula to calculate roots of the eqn given above which solves down to i.e x^2+2x-288=0 where I got stuck trying to find the square root of 1156 (its 34 btw). In retrospect I would set up the eqn and start plugging in values to solve it. when you plug D it satisfies the eqn which boils down to 12*(3/4-2/3) = 1 = RHS of I The only trick in this is that it gives the value of x which is the total number of eggs before the cook bargained his way to getting more. The answer that the question is looking for is really x+2=18 since it says how many did the cook go home with? (hands up if you missed that part!) hence E _________________ Champions aren't made in the gyms. Champions are made from something they have deep inside them -- a desire, a dream, a vision. Intern Joined: 02 Feb 2011 Posts: 7 Followers: 0 Kudos [?]: 0 [0], given: 1 A question from diagnostic test [#permalink] 06 Feb 2011, 17:56 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?

Answer is 18, but I did not get the explanation.
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Re: A question from diagnostic test [#permalink]  07 Feb 2011, 02:48
Yeah, this one is a bit tricky. Our equation we want will look like

Price per dozen before - Price per dozen after (we got the two eggs) = 1 (the difference was 1$) How do we find the price per dozen? One way is taking the unit price and multiply by 12 (total price/no of eggs) * 12 = price per dozen let x denote no of eggs and total price was 12$

(12/x)*12 = dozen price before we got the two eggs for free
(12/x+2)*12 = dozen price after we got the two eggs for free, and the difference should be 1 so.

(12/x)*12 - (12/x+2)*12 = 1

12/x -12/(x+2) =1/12
12(x+2)-12(x) = ((x)(x+2))/12
12x+24-12x = (x^2 +2x)/12
x^2 +2x -288 = 0
x(x+2) - 288 = 0

288 is approximately ~17^2 so we need something near that

18(20) = 360 too much
16(18) = 288 so x is 16 and we will bring home x+2 eggs = 18
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Re: A cook [#permalink]  07 Feb 2011, 04:43
Let x be the number of eggs initially bought.

x eggs $$\rightarrow$$ $12 1 egg $$\rightarrow$$ (12/x) 12 eggs $$\rightarrow$$ (12*12)/x = 144/x After adding two eggs (x+2)eggs $$\rightarrow$$$12
1 egg $$\rightarrow$$ 12/(x+2)
12 eggs $$\rightarrow$$ 12*12/(x+2) = 144/(x+2)

$$\frac{144}{(x+2)}+1=\frac{144}{x}$$
$$x^2+2x-288=0$$
$$(x-16)(x+18)=0$$

x=16 and x=-18

Count can't be minus;

Eggs initially purchased = 16. After adding 2 = 16+2=18

Ans: "E"
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Re: A cook [#permalink]  07 Feb 2011, 05:05
Hi
I have a doubt in this with my approach.

Let us assume price per dozen of eggs is x, and he bought total y eggs. So he bought y/12 dozens of eggs.

Now we can have 2 equations :

y/12 * x = 12

and

(y+2)/12 * (x-1) = 12

Regards,
Subhash
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Re: A cook [#permalink]  07 Feb 2011, 05:21
subhashghosh wrote:
Hi
I have a doubt in this with my approach.

Let us assume price per dozen of eggs is x, and he bought total y eggs. So he bought y/12 dozens of eggs.

Now we can have 2 equations :

y/12 * x = 12

and

(y+2)/12 * (x-1) = 12

Regards,
Subhash

Your interpretation is correct. and y will not be equal to 18. It will be 16.

y/12 * x = 12
x = 144/y

(y+2)/12 * ((144/y)-1)=12
This gets transformed into same equation;
$$y^2+2y-288=0$$

Solve for roots;

y=16 or y=-18

y can't be negative.

y=16.

y- number of eggs initially purchases = 16
After adding 2 eggs to this
16+2=18.
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Re: A question from diagnostic test [#permalink]  07 Feb 2011, 19:51
Expert's post
sara933 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? Answer is 18, but I did not get the explanation. Another approach: Let us say the price per dozen is p. Since he paid a total of$12, he must have bought 12/p dozens.
Total number of eggs = $$(\frac{12}{p})*12$$(because a dozen has 12 eggs)
But, he got 2 extra eggs so now total number of eggs = $$(\frac{12}{p})*12 + 2$$

The price per dozen went down by $1 so new price per dozen = (p - 1) New total number of eggs = $$\frac{12}{(p-1)} * 12$$ $$(\frac{12}{p})*12 + 2 = \frac{12}{(p-1)} * 12$$ We see that we have numerator 144 and denominator p on one side and (p-1) on the other side. Since these are number of eggs, they must be integral values. $$144 = 2^4*3^2$$ We need two consecutive integers both of which divide 144. You can see that 8 and 9 both divide 144. Let's confirm: $$(\frac{12}{9})*12 + 2 = \frac{12}{8} * 12 = 18$$ So the cook brought 18 eggs home. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: GMAT Diagnostic Test Question 27 [#permalink]  17 Apr 2011, 18:53
price per dozen difference is 1

144/x - 144(x+2) = 1

solving we get x = 16

=> x+2 = 18

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Re: GMAT Diagnostic Test Question 27 [#permalink]  17 Apr 2011, 23:11
im having trouble understanding how multiplying $$\frac{1}{12}$$ reduces the price per dozen by a dollar?
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Re: A cook [#permalink]  15 Jun 2011, 03:55
I stopped at 16 without adding 2 more eggs. Now i know my mistake. Good Question
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Re: A cook [#permalink]  15 Jun 2011, 23:36
n/12 = no of dozens

thus 12/(n/12) - 12/[(n+2)/12] = 1

144/n - 144/n+2 = > n = 16

thus 18
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Re: GMAT Diagnostic Test Question 27 [#permalink]  04 Sep 2011, 05:28
As long as we understand that the cook gets the 2 additional eggs at the same price of 12, we can setup an equation

N- Number of eggs
P - Price per dozen

12 eggs cost $P N eggs cost NP/12 and this = 12 --- 1st equation Now 12 eggs cost$P-1
N+2 eggs cost (N+2)(P-1)/12 and this = 12 ---2nd equation. Here,we know that the cook got the 2 eggs for the same amount of $12 Combining both equations, we have NP=(N+2)(P-1) NP = 144 Finally, we get N^2+2N-288=0. Solving this equation, we get N=16. Therefore, the number the cook took back home is 18 Intern Joined: 20 Oct 2011 Posts: 5 Followers: 0 Kudos [?]: 0 [0], given: 3 Re: GMAT Diagnostic Test Question 27 [#permalink] 25 Oct 2011, 15:54 urchin wrote: my approach..... Let him buy m number of eggs.... so when the prize came down by 1$ per 12 eggs that means per egg it came down by 1/12.
so equation becomes...
12/m = 12/(m+2) + 1/12

....... 12/m ---- original price per egg
12/(m+2) --- new price per egg
1/12 -- the amount by which the new price per egg came down.

U can now subsitute the values given in option and come at the ans.

Hi , I do find your approach to fit more my way of thinking and approaching this problem but... and I apologize if this is very stupid, but I'm substituting 18 on the final formula, and can't get prove that it is correct....

is 12/18 equal to 12/20 + 1/12 ?? .. ..

what am I doing wrong?
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Re: GMAT Diagnostic Test Question 27 [#permalink]  05 Jan 2012, 05:19
N= Number of dozen;
X= price per dozen;

NX=12
(N+1/6)(X-1)=12

Solving for N we get N=4/3
The total number of eggs = 4/3*12+2=18

Can anyone solve it???? I do not get N=4/3.

Thanks!
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Re: GMAT Diagnostic Test Question 27 [#permalink]  14 Aug 2013, 15:34
powerka wrote:
Target760 wrote:
here is my solution:

let's say no of eggs purchased = E

price per dozen of eggs in first case = ($12/E)*12 i.e. price per egg multiply by 12, to get price per dozen new price per dozen = ($12/[E+2])*12

now, the equation is; (old price per dozen) - (new price per dozen) = 1

i.e. {($12/E)*12} - {($12/[E+2])*12} = 1

solve for E, 144/E - 144/(E+2) = 1

144E + 288 - 144E = E(E+2)

288=E^2 +2E

E^2 + 2E - 288 = 0

By factoring we get
E^2 + 18E - 16E -288 = 0
E(E+18)-16(E+18)=0
(E+18)(E-16)=0
E= - 18, or 16

rejecting negative value we get E=16 (the original no of eggs purchased)

no. of eggs brought home = E+2 or 16 + 2 = 18

Actually, I used the same approach, but did not dare to do the factorization on the timed question, so I used the quadratics formula.

E^2 + 2E - 288 = 0

E = {-2 +/- sqrt[4 - 4*(-288)]}/2 => {-2 +/- sqrt[1156]}/2 => {-2 +/- 34}/2 => E =16
=> E+2 = 18

Of course, I wasted precious time finding the square root of 1156. I find both methods (quadratics vs factorization) equally cumbersome for this equation.

You spent some extra time getting to 1156 and then sqrting it. Would have been more efficient to do 4+4(288) in the radical, which leads to 4(1+288) = (2^2)(17^2). Much quicker.
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Re: GMAT Diagnostic Test Question 27 [#permalink]  16 Sep 2013, 23:16
prateekbhatt wrote:
dzyubam wrote:
Explanation:
 Rating:

This is a hard equation to come up with during the test. The price of eggs was \$12. Let $$E$$ denote the number of eggs and $$P$$ denote the price.

$$(E+2)\times(P-\frac{1}{12})=12$$

From this equation we get that $$E = 16$$.

Answer: $$E+2=16+2=18$$.

This equation is much more easier than the rest. But definately a 750 level ques.

Honestly, I do not understand $$(P-\frac{1}{12})$$...

Secondly, how do you solve from $$(E+2)\times(P-\frac{1}{12})=12$$ -->$$E = 16$$ - with this "shortcut" it is pretty much useless. Please explain to me how it could be solved, with two variables...Thanks.
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Re: GMAT Diagnostic Test Question 27   [#permalink] 16 Sep 2013, 23:16

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# GMAT Diagnostic Test Question 26

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