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GMAT Diagnostic Test Question 26

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Math Expert
Joined: 02 Sep 2009
Posts: 23357
Followers: 3604

Kudos [?]: 28727 [0], given: 2824

Re: GMAT Diagnostic Test Question 27 [#permalink]  16 Sep 2013, 23:48
Expert's post
obs23 wrote:
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. Please refer to official solution: gmat-diagnostic-test-question-79356-40.html#p1257091 _________________  Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes Intern Joined: 18 Jan 2014 Posts: 8 Concentration: Technology, General Management GMAT Date: 04-28-2014 WE: Information Technology (Insurance) Followers: 0 Kudos [?]: 5 [0], given: 1 Re: GMAT Diagnostic Test Question 26 [#permalink] 10 Mar 2014, 13:48 Can anyone refer me to similar problems so I can practice this type of problem? Thanks. Intern Joined: 25 Sep 2013 Posts: 5 Concentration: Finance, International Business GMAT 1: 720 Q50 V37 Followers: 0 Kudos [?]: 1 [0], given: 133 Re: GMAT Diagnostic Test Question 26 [#permalink] 17 Jul 2014, 01:01 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

First, I noticed that this problem was about averages. Thus, I recalled the formula A = \frac{S}{n}, and could quickly set up 2 equations.

equation #1 ... A = \frac{12}{n}
equation #2 ... A - \frac{1}{12} = \frac{12}{{n+2}} ( the price per dozen went down by 1 dollar --> the price per egg went down by \frac{1}{12} dollar)

Secondly, I combined the 2 equations, resulting in

\frac{12}{n} = \frac{12}{{n+2}} + \frac{1}{12}

144 * (n+2) - 144 * n = n * (n+2)

288 = n * (n+2)

At this point I was done, and knew that the answer was 18 because of a "shortcut", which I remembered from calculation squares!
You might want to remember that "shortcut":
n^2 = (n - x) * (n + x) +x^2

Examples:
17^2= (17 - 1) * (17 + 1) + 1^2 --> 289 = 16 * 18 + 1 --> 288 = 16 * 18
17^2= (17 - 2) * (17 + 2) + 2^2
17^2= (17 - 3) * (17 + 3) + 3^2
(hint: It is the last one, which is generally useful IRL )

Generally, using this "shortcut" has been very helpful in solving a couple of difficult questions!
Finally, I hope that my answer was helpful and would kindly welcome kudos.

Thanks,
Johannes
Re: GMAT Diagnostic Test Question 26   [#permalink] 17 Jul 2014, 01:01
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