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# GRE Weekly Challenge #5

Author Message
Senior Manager
Joined: 25 Jul 2011
Posts: 298
Location: India
Concentration: Strategy, General Management
GMAT 1: 730 Q50 V40
GPA: 3
WE: Operations (Non-Profit and Government)
Followers: 28

Kudos [?]: 218 [0], given: 286

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02 Oct 2011, 11:07
GMAT Club invites you to test your GRE knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GRE Strategy guide. What are you waiting for? Get out your scrap paper and start solving! Click here to view contest & prize details

This week's question:
Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?
A.) 2
B.) 3
C.) 4
D.) 5
E.) 6

Edit: This challenge is now closed

Solution
Let’s use x for the number of cookies produced by the original recipe, and y for the weight of each of the cookies. Given those variables, our first equation is simply xy = 600. We also need to create an equation that represents the new recipe. Since the number of cookies produced has increased by 30, and the weight of each cookie has decreased by 1, the new equation is (x + 30)(y – 1) = 600. Remember, the total weight is still 600 ounces. Foiling this equation yields xy – x + 30y – 30 = 600.
We now have two equations with two variables. There are several different paths we can go down here, but all involve substitution of one of the variables, and all will yield a quadratic. The simplest path is to recognize that since xy = 600, we can substitute for xy in the second equation to get 600 – x + 30y – 30 = 600. Subtracting the 600 from both sides, and adding an x to each side gives us 30y – 30 = x. We can now substitute for x in the first equation.
xy = 600 → y(30y – 30) = 600. This gives us 30y2 – 30y = 600.
Next divide both sides by 30 and set the equation to zero: y2 – y – 20 = 0.
Now that the equation is set to zero, we can factor it into its roots: (y + 4)(y – 5) = 0
The weight of the original cookies was thus 5 ounces, or -4 ounces. The negative root is a nonsensical result given the constraints of the problem, so the answer is 5 ounces.
An alternate solution would be to start with each answer choice, and see which satisfies the conditions of the problem. To implement this method, it’s helpful to set up a chart.

From the chart we can see that only in answer D will we end up with 30 additional cookies after changing the recipe.

The winner of this Week's Challenge is... (drum roll).... pitpit. Congratulations! Please send me a pm with your shipping address, and choice of Manhattan GRE Guide

Details of next week's competition will be posted in the Weekly Challenge Master thread... Stay tuned!
_________________

Last edited by rasta on 05 Oct 2011, 09:59, edited 1 time in total.
Posted Winner & Solution
Manager
Joined: 03 Mar 2011
Posts: 90
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 2

Kudos [?]: 144 [0], given: 12

Re: GRE Weekly Challenge #5 [#permalink]

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03 Oct 2011, 11:37
This reply is hidden until the winner is announced.
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Manager
Status: Still Struggling
Joined: 03 Nov 2010
Posts: 137
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 93 [0], given: 8

Re: GRE Weekly Challenge #5 [#permalink]

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03 Oct 2011, 12:51
This reply is hidden until the winner is announced.
_________________

Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)

Manager
Joined: 12 Aug 2011
Posts: 95
Location: United States (SC)
Concentration: Operations, General Management
Schools: Cornell (Johnson) - Class of 2014
GMAT 1: 710 Q48 V39
Followers: 0

Kudos [?]: 15 [0], given: 1

Re: GRE Weekly Challenge #5 [#permalink]

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03 Oct 2011, 14:06
This reply is hidden until the winner is announced.
Intern
Joined: 26 Aug 2011
Posts: 6
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: GRE Weekly Challenge #5 [#permalink]

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03 Oct 2011, 16:20
This reply is hidden until the winner is announced.
Manager
Joined: 24 Nov 2010
Posts: 210
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 83 [0], given: 7

Re: GRE Weekly Challenge #5 [#permalink]

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03 Oct 2011, 19:51
This reply is hidden until the winner is announced.
Manager
Status: Back to (GMAT) Times Square!!!
Joined: 15 Aug 2011
Posts: 179
Location: United States (IL)
GMAT 1: 650 Q49 V30
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 79 [0], given: 25

Re: GRE Weekly Challenge #5 [#permalink]

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04 Oct 2011, 01:52
This reply is hidden until the winner is announced.
_________________

Working towards a goal...
V.

Intern
Joined: 04 Oct 2011
Posts: 1
Followers: 0

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

Re: GRE Weekly Challenge #5 [#permalink]

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04 Oct 2011, 14:30
This reply is hidden until the winner is announced.
Re: GRE Weekly Challenge #5   [#permalink] 04 Oct 2011, 14:30
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