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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]
30 Nov 2009, 22:44
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
hi flying bunny, how did you get XY=12? i get X=price/dozen, and there are Y dozen, but how does that equate to 12? thanks!
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Re: GMAT Diagnostic Test Question 27 [#permalink]
04 Jan 2010, 21:57
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 - $0.66 = ~8 cents in savings. This is a good approach, solving it the other direction.
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Re: GMAT Diagnostic Test Question 27 [#permalink]
11 Jan 2010, 00:21
marcos4 wrote: Quote: suppose before added two more eggs, the price per dozen is X and there are Y dozen
so we have XY=12
and (X-1)(Y+1/6)=12
from above we can get Y=16/12, there are 16 eggs.
in the end, the cook brings 16+2=18 eggs home.
Hello, I feel that flyingbunny's way is the simplest but there's one part I don't get it. Quote: we have XY=12 OK Quote: (X-1) means in regular english "the price per dozen was reduced by 1$" 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.
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Thanks a lot Whipplash. Your explanation is much easier to understand.
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John went to the super market and bought some apples for 12$ , at the check out counter the cashier said he can have 2 more free apples. As a result the price per dozen went down by 1 $ . How many apples did he get home 8 12 16 18 20
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This is the same problem that someone else posted yesterday. Kindly check out the problem that's titled "A cook" in the forum.
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this is a good explnation i was going on the same lines but i mad a mistake of making n /12 as cost per egg
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Re: GMAT Diagnostic Test Question 27 [#permalink]
22 Sep 2010, 04:39
dzyubam wrote: Explanation:
Official Answer: E(E+2)\times(P-\frac{1}{12})=12From this equation we get that E = 16. Answer: E+2=16+2=18. How did you solve an equation with 2 variables?
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GMAT Club Diagnostic Test- Tough PS Problem [#permalink]
24 Sep 2010, 12:59
This is a tough problem that the provided solution some up with an equation which is admittedly difficult to derive. Does anyone know a quicker means to solve this problem??
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?
-8
-12
-15
-16
-18
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I will go with option E)18
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Nice approach whitesplash
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Re: GMAT Diagnostic Test Question 27 [#permalink]
09 Oct 2010, 07:54
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
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Re: GMAT Diagnostic Test Question 27 [#permalink]
02 Nov 2010, 21:10
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
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Re: GMAT Diagnostic Test Question 27 [#permalink]
05 Jan 2011, 09:38
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
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A question from diagnostic test [#permalink]
06 Feb 2011, 18:56
A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?
Answer is 18, but I did not get the explanation.
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Re: A question from diagnostic test [#permalink]
07 Feb 2011, 03:48
Yeah, this one is a bit tricky. Our equation we want will look like Price per dozen before - Price per dozen after (we got the two eggs) = 1 (the difference was 1$) 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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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)=0x=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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