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GMAT Diagnostic Test Question 26

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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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
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A question from diagnostic test [#permalink] New post 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] New post 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] New post 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] New post 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

But this does not give y = 18 , could someone please help me ?

Regards,
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Re: A cook [#permalink] New post 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

But this does not give y = 18 , could someone please help me ?

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] New post 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.
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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

Answer is E.
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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] New post 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] New post 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] New post 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
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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] New post 15 Nov 2011, 18:16
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


clear as crystal explanation :D
thanksssss
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 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] New post 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

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.


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] New post 15 Aug 2013, 01:59
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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 --> \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.
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Re: GMAT Diagnostic Test Question 27 [#permalink] New post 16 Sep 2013, 23:16
prateekbhatt wrote:
dzyubam wrote:
Explanation:
Rating:

Official Answer: E

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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