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GMAT Diagnostic Test Question 27 [#permalink]
 06 Jun 2009, 23:08
GMAT Diagnostic Test Question 27Field: word problems Difficulty: 750
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
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Re: GMAT Diagnostic Test Question 27 [#permalink]
06 Jul 2009, 06:48
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Explanation:
Official Answer: EThis 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})=12From this equation we get that E = 16. Answer: E+2=16+2=18.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
15 Jul 2009, 22:09
very tough...any alternate way of solving?
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Re: GMAT Diagnostic Test Question 27 [#permalink]
24 Jul 2009, 05:37
P indicates the price per dozen?
In that case shouldnt you take (P-1) to multiply with (e+2)?
How did you come up with (P- 1/12)?
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Re: GMAT Diagnostic Test Question 27 [#permalink]
25 Jul 2009, 10:48
You could plug in numbers......just start with E or D first....
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Re: GMAT Diagnostic Test Question 27 [#permalink]
26 Jul 2009, 10:36
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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
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Re: GMAT Diagnostic Test Question 27 [#permalink]
27 Jul 2009, 01:38
A very good one! +1. 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
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Re: GMAT Diagnostic Test Question 27 [#permalink]
31 Jul 2009, 16:12
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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.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
20 Aug 2009, 08:10
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
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Re: GMAT Diagnostic Test Question 27 [#permalink]
21 Aug 2009, 23:17
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my way: 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.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
22 Aug 2009, 15:44
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defoue wrote:
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
Need to factors of 288 that when subtracted render 2. Prime factorization of 288 gives: 2x2x2x2x2x3x3 Try combining primes to get two numbers whose difference is 2. There are 7 primes, so one number would have 3 primes and the other 4 primes. First combinations to try would be 3x3x2 and 2x2x2x2. That's 18 and 16. 18-16=2. Bingo, we got the factors we were looking for.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
22 Aug 2009, 15:51
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 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.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
23 Aug 2009, 12:50
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Flyingbunny's method is the fastest, as by working by dozens instead of units it results in smaller numbers and simpler calculations. Thumbs up for him. Allow me to recap the 3 methods herein presented using the same nomenclature. A-Target760's Uses equation: {($12/E)*12} - {($12/[E+2])*12} = 1 ...it results in E^2+2E-288=0 B-dzyubam's Uses equations: 1. EP=12 2. (E+2)(P-(1/12))=12 ...it results in E^2+2E-288=0 C-flyingbunny's Uses equations: 1. EP=12 2. (E+(1/6))(P-1)=12 .....it resutls in 6E^2+E-12=0. Easier to find the root than with other methods.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
23 Aug 2009, 18:14
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nice summary and thanks.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
22 Oct 2009, 12:29
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my approach..... Let him buy m number of eggs.... so when the prize came down by 1$ 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.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
07 Nov 2009, 08:29
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} - {($12/[E+2])*12} = 1
solve for E, 144/E - 144/(E+2) = 1
144E + 288 - 144E = E(E+2)
288=E^2 +2E
E^2 + 2E - 288 = 0
By factoring we get
E^2 + 18E - 16E -288 = 0
E(E+18)-16(E+18)=0
(E+18)(E-16)=0
E= - 18, or 16
rejecting negative value we get E=16 (the original no of eggs purchased)
no. of eggs brought home = E+2 or 16 + 2 = 18
Therefore, answer is E A killer in disguise! I used this approach as well (post test of course, got it wrong in the test)
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Re: GMAT Diagnostic Test Question 27 [#permalink]
09 Nov 2009, 23:47
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N= Number of dozen;
X= price per dozen;
NX=12
(N+1/6)(X-1)=12
Solving for N we get N=4/3
The total number of eggs = 4/3*12+2=18
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Re: GMAT Diagnostic Test Question 27 [#permalink]
13 Nov 2009, 10:40
I got it. But took 6 min and had to resort to backsolving. Brutal.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
21 Nov 2009, 05:13
I solved it all the way till X^2 + 2X +288 =0; then gave up and guess
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Re: GMAT Diagnostic Test Question 27 [#permalink]
26 Nov 2009, 21:26
Quote: suppose before added two more eggs, the price per dozen is X and there are Y dozen
so we have XY=12
and (X-1)(Y+1/6)=12
from above we can get Y=16/12, there are 16 eggs.
in the end, the cook brings 16+2=18 eggs home.
Hello, I feel that flyingbunny's way is the simplest but there's one part I don't get it. Quote: we have XY=12 OK Quote: (X-1) means in regular english "the price per dozen was reduced by 1$" Quote: (X-1)(Y+1/6)=12
Where does this 1/6 comes from ? Thanks !
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Re: GMAT Diagnostic Test Question 27
[#permalink]
26 Nov 2009, 21:26
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