GRE Weekly Challenge #5

Question

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 Please post your answer, along with the explanation, below. Get cracking!

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. https://img835.imageshack.us/img835/8885/mgreexplanation.jpg From the chart we can see that only in answer D will we end up with 30 additional cookies after changing the recipe. The correct answer is D. 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!

bagrettin · Answer

Let denote the amount of cookie dough which is needed to make 1 cookie by x.

Then initially Cape Cod Cookies could make  \frac{600}{x}  cookies.
Now for one cookie he needs  (x-1)  ounces of dough.
Therefore he is able to produce  \frac{600}{x-1}  cookies.

These two numbers are different by 30.
Finally, we get the following equation:
 \frac{600}{x}+30=\frac{600}{x-1} 
 600(x-1)+30x(x-1)=600x 
 600x-600+30x^2-30x=600x 
 30x^2-30x-600=0 
 x^2-x-20=0 
 x=5  or  x=-4 .
Obviously,  x>0 , so we choose  x=5

Each cookie originally weighs 5 ounces.
The answer is (D)

krishnasty · Answer

IMO D...Ans : 5 ounces

Let the original weight be x ounce
The total number of cookies = n

new weight : (x-1) ounce
new count of cookied = n+30

now, according to the equation,
600= xn = (x-1)(n+30)

solving both the equations, we get x =5

pitpit · Answer

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

x= initial number of cookies (cookie)
y= initial weight per cookie (oz/cookie)

Write two equations 
x*y=600
(30+x)*(y-1)=600

Solve using system of equations 
x*y=(30+x)*(y-1)
xy=30y-30+xy-x
30=30y-x

Subsititute in x=600/y 
30=30y-600/y

Multiply both sides by y 
30y=30y^2-600

Simplify 
y=y^2-20
y^2-y-20=0

Factor 
(y-5)(y+4)=0
Solutions for y are 5 and -4. Since the weight cannot be negative, the original weight was  5 ounces.

SOLUTION: D) 5

guanabana · Answer

The answer is  D.) 5 . I used the plugin strategy for this one:

Plugin 4 for the cookie weight, it makes 600/4 = 150 cookies. With the new weight 3, it makes 600/3 = 200 cookies with over 50 cookies, not the 30 we want.

Plugin 5 for the cookie weight, it makes 120 cookies. With the new weight 4, it makes 150 cookies with exactly 30 cookies extra. So the original cookie weight was 5.

dreambeliever · Answer

let x be the initial wt.
from the question:
600/x = 600/(x-1) - 30
--> 20/x = 20/(x-1) -1
--> x^2 + x - 20 = 0
--> x= -5 or x = 4 
since x cannot be -5, x = 4
Ans c

vix · Answer

The best way to solve this problem is to backsolve:

Take option (C) 4,

If 4 is right answer, then as per question 4*N = 600 where N is number of cookies made from dough.
Hence N = 150.

Now, weight is less by one ounce, therefore, 4-1=3 is weight hence number of cookies will be = 600/3=200, giving difference as 200-150=50, but the given difference is 30, hence 4 is not the right choice.

Take option (D) 5,
If 5 is right answer, then as per question 5*N = 600 where is N is number of cookies made from dough.
Hence N = 120.

Now, weight is less by one ounce, therefore, 5-1=4 is weight hence number of cookies will be = 600/4=150, which is 150-120=30, and the given difference is 30, hence 5 is the right choice.

Answer – (D) 5.

Alternative method:

Let number of cookies from 1 dough batch = N
Weight of each cookie = x

Therefore, N*x = 600 ....(i)

When weight reduces by 1 ounce, the number of cookies increases by 30.
Therefore, (N+30)*(x-1) = 600 ….(ii)

Equating both –>

N*x = (N+30)*(x-1) 
N*x = N*x – N + 30*x -30
Canceling N*x from both sides,
N = 30*(x-1)

Replacing this value of N in equation ..(i) 
30*(x-1)*x = 600
x*(x-1) = 20

we need 2 number which on multiplying give 20, they are 4 and 5, hence from equation ..(i) x = 5.

Answer – (D) 5.

TheSlothMan · Answer

The answer is D) 5.

Reasoning
1oz cookies-600 cookies
2oz cookies-300 cookies
3oz cookies-200 cookies
4oz cookies-150 cookies
5oz cookies-120 cookies
6oz cookies-100 cookies

The extra 30 cookies can be easily seen as resulting from the decrease from 5oz to 4oz product.

GRE Weekly Challenge #5

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