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# GMAT Diagnostic Test Question 26

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GMAT Diagnostic Test Question 26 [#permalink]

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06 Jun 2009, 23:08
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GMAT Diagnostic Test Question 26
Field: word problems
Difficulty: 750

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 _________________ i love kudos consider giving them if you like my post!! CRITICAL REASONING FOR BEGINNERS: notes & links to help you learn CR better. Click Below http://gmatclub.com/forum/critical-reasoning-for-beginners-82111.html QUANT NOTES FOR PS & DS: notes to help you do better in Quant. Click Below http://gmatclub.com/forum/quant-notes-for-ps-ds-82447.html GMAT Timing Planner: This little tool could help you plan timing strategy. Click Below http://gmatclub.com/forum/gmat-cat-timing-planner-82513.html Manager Joined: 14 Aug 2009 Posts: 123 Followers: 2 Kudos [?]: 100 [11] , given: 13 Re: GMAT Diagnostic Test Question 27 [#permalink] ### Show Tags 21 Aug 2009, 23:17 11 This post received KUDOS 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. _________________ Kudos me if my reply helps! Intern Joined: 31 Jul 2009 Posts: 2 Followers: 0 Kudos [?]: 8 [8] , given: 0 Re: GMAT Diagnostic Test Question 27 [#permalink] ### Show Tags 31 Jul 2009, 16:12 8 This post received KUDOS 1 This post was BOOKMARKED 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. Manager Joined: 22 Jul 2009 Posts: 191 Followers: 4 Kudos [?]: 252 [6] , given: 18 Re: GMAT Diagnostic Test Question 27 [#permalink] ### Show Tags 23 Aug 2009, 12:50 6 This post received KUDOS 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. _________________ Please kudos if my post helps. Ms. Big Fat Panda Status: Three Down. Joined: 09 Jun 2010 Posts: 1922 Concentration: General Management, Nonprofit Followers: 440 Kudos [?]: 1909 [5] , given: 210 Re: A cook [#permalink] ### Show Tags 21 Jul 2010, 11:02 5 This post received KUDOS Let us assume he buys n eggs and it costs him$12. So the cost per egg = $$\frac{12}{n}$$.

Cost per dozen eggs at the original price = $$\frac{12}{n}*12$$ = $$\frac{144}{n}$$. (Since there are 12 eggs in a dozen and we are multiplying the cost per egg calculated above with 12)

Original Cost per dozen = $$\frac{144}{n}$$

Now, the number of eggs he buys becomes n+2, and the cost remains the same. So the cost per egg is now: $$\frac{12}{n+2}$$.

Using the same logic, cost per dozen = Cost per egg * 12 = $$\frac{12}{n+2}*12 = \frac{144}{n+2}$$.

New Cost per dozen = $$\frac{144}{n+2}$$

It's given that the new cost per dozen = original cost per dozen - 1

$$\frac{144}{n+2}=\frac{144}{n} - 1$$

So you get: $$\frac{144}{n} - \frac{144}{n+2} = 1$$

Cross multiplying: $$144( \frac{1}{n} - \frac{1}{n+2}) = 1$$

$$( \frac{1}{n} - \frac{1}{n+2}) = \frac{1}{144}$$

$$\frac{n+2 - n}{(n)(n+2)} = \frac{1}{144}$$

$$288 = n(n+2)$$

Solving this you get 18.

Alternatively plugging numbers will work faster. Just find out cost per dozen for each of the numbers and compare them to get answer.
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Re: GMAT Diagnostic Test Question 27 [#permalink]

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06 Jul 2009, 06:48
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Explanation:

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 $$\frac{144}{16}-\frac{144}{18}=9-8=1$$.

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Last edited by bb on 29 Sep 2013, 15:27, edited 2 times in total.
Updated
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Re: GMAT Diagnostic Test Question 27 [#permalink]

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22 Oct 2009, 12:29
4
KUDOS
my approach.....
Let him buy m number of eggs....
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 Intern Joined: 13 May 2010 Posts: 5 Followers: 1 Kudos [?]: 2 [1] , given: 2 A cook [#permalink] ### Show Tags 21 Jul 2010, 10:57 1 This post received KUDOS 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]

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15 Aug 2013, 02:59
1
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Expert's post
SOLUTION:

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} - {($12/[E+2])*12} = 1 solve for E, 144/E - 144/(E+2) = 1 144E + 288 - 144E = E(E+2) 288=E^2 +2E E^2 + 2E - 288 = 0 By factoring we get E^2 + 18E - 16E -288 = 0 E(E+18)-16(E+18)=0 (E+18)(E-16)=0 E= - 18, or 16 rejecting negative value we get E=16 (the original no of eggs purchased) no. of eggs brought home = E+2 or 16 + 2 = 18 Therefore, answer is E Actually, I used the same approach, but did not dare to do the factorization on the timed question, so I used the quadratics formula. E^2 + 2E - 288 = 0 E = {-2 +/- sqrt[4 - 4*(-288)]}/2 => {-2 +/- sqrt[1156]}/2 => {-2 +/- 34}/2 => E =16 => E+2 = 18 Of course, I wasted precious time finding the square root of 1156. I find both methods (quadratics vs factorization) equally cumbersome for this equation. _________________ Please kudos if my post helps. Manager Joined: 22 Sep 2009 Posts: 222 Location: Tokyo, Japan Followers: 2 Kudos [?]: 21 [0], given: 8 Re: GMAT Diagnostic Test Question 27 [#permalink] ### Show Tags 21 Nov 2009, 05:13 I solved it all the way till X^2 + 2X +288 =0; then gave up and guess Intern Joined: 06 Nov 2009 Posts: 4 Followers: 0 Kudos [?]: 1 [0], given: 2 Re: GMAT Diagnostic Test Question 27 [#permalink] ### Show Tags 26 Nov 2009, 21:26 Quote: suppose before added two more eggs, the price per dozen is X and there are Y dozen so we have XY=12 and (X-1)(Y+1/6)=12 from above we can get Y=16/12, there are 16 eggs. in the end, the cook brings 16+2=18 eggs home. Hello, I feel that flyingbunny's way is the simplest but there's one part I don't get it. Quote: we have XY=12 OK Quote: (X-1) means in regular english "the price per dozen was reduced by 1$"

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]

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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!
Re: GMAT Diagnostic Test Question 27   [#permalink] 30 Nov 2009, 22:44

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# GMAT Diagnostic Test Question 26

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