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DS - Determining Ratio

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DS - Determining Ratio

by karthikpandian19 » Wed Jul 11, 2012 7:10 pm
Jackie and Micah each bake 10 cookies using two different recipes. If they use a total of 15n grams of sugar between them, what is the ratio of the amount of sugar in each of Micah's cookies to the amount of sugar in each of Jackie's cookies?

1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
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by eagleeye » Thu Jul 12, 2012 5:31 am
karthikpandian19 wrote:Jackie and Micah each bake 10 cookies using two different recipes. If they use a total of 15n grams of sugar between them, what is the ratio of the amount of sugar in each of Micah's cookies to the amount of sugar in each of Jackie's cookies?

1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
Let sugar amount in each of Micah's cookies be x and that by Jackie's be y.

Then we are told that 10x+10y = 15n.
=> x+y = 3n/2
We need to find x/y.

With that in mind let's look at the statements:
1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
So in other words, 9n/x - 9n/y = 5
=> 9n(1/x-1/y) = 5
=> 1/x-1/y = 5/(9n)
Multiplying this equation with the original, we get
(x+y)(1/x-1/y) = 3n/2*5/(9n)
=> (x+y)(y-x)/(xy) = 5/6
=> (y^2-x^2)/(xy) = 5/6
=> 6y^2-6x^2 = 5xy
=> 6y^2-5xy-6x^2=0
=> 6y^2-6xy +xy-6x^2=0
=> 6y(y-6x) + x(y-6x)=0
=> (6y+x)(y-6x)=0
Either y-6x = 0 or 6y+x =0.

y=6x => x/y = 1/6. (6y+x = 0 means that x=-6y which means that one value is negative which is impossible here). Hence x/y =1/6.
Sufficient.

2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
This just tells us that x==144/12 = 12. we still need to find either n and y to find y to determine x/y. Insufficient.

Hence A.
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by karthikpandian19 » Thu Jul 12, 2012 1:10 pm
OA is A
eagleeye wrote:
karthikpandian19 wrote:Jackie and Micah each bake 10 cookies using two different recipes. If they use a total of 15n grams of sugar between them, what is the ratio of the amount of sugar in each of Micah's cookies to the amount of sugar in each of Jackie's cookies?

1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
Let sugar amount in each of Micah's cookies be x and that by Jackie's be y.

Then we are told that 10x+10y = 15n.
=> x+y = 3n/2
We need to find x/y.

With that in mind let's look at the statements:
1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
So in other words, 9n/x - 9n/y = 5
=> 9n(1/x-1/y) = 5
=> 1/x-1/y = 5/(9n)
Multiplying this equation with the original, we get
(x+y)(1/x-1/y) = 3n/2*5/(9n)
=> (x+y)(y-x)/(xy) = 5/6
=> (y^2-x^2)/(xy) = 5/6
=> 6y^2-6x^2 = 5xy
=> 6y^2-5xy-6x^2=0
=> 6y^2-6xy +xy-6x^2=0
=> 6y(y-6x) + x(y-6x)=0
=> (6y+x)(y-6x)=0
Either y-6x = 0 or 6y+x =0.

y=6x => x/y = 1/6. (6y+x = 0 means that x=-6y which means that one value is negative which is impossible here). Hence x/y =1/6.
Sufficient.

2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
This just tells us that x==144/12 = 12. we still need to find either n and y to find y to determine x/y. Insufficient.

Hence A.
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Karthik
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by GMATGuruNY » Thu Jul 12, 2012 1:13 pm
karthikpandian19 wrote:Jackie and Micah each bake 10 cookies using two different recipes. If they use a total of 15n grams of sugar between them, what is the ratio of the amount of sugar in each of Micah's cookies to the amount of sugar in each of Jackie's cookies?

1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
Statement 1: Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
Case 1: Micah needs 9n grams to make 10 cookies, Jackie needs 9n grams make 5 cookies.
Thus, for Jackie to make 10 cookies -- twice the number of cookies here -- she will need twice the amount of sugar (18n).
Too much: 15n grams must be sufficient to make 20 cookies (10 for Micah, 10 for Jackie).

Case 2: Micah needs 9n grams to make 15 cookies, Jackie needs 9n grams to make 10 cookies.
Thus, for Micah to make 10 cookies -- 2/3 the number of cookies here -- he will need 2/3 the amount of sugar:
2/3 * 9n = 6n.
This works:
To make 10 cookies each, Micah's amount + Jackie's amount = 6n + 9n = 15n.

The progression here implies the following:
If the number of cookies INCREASES beyond the values in Case 2, the amount of sugar required by Jackie and Micah to make 10 cookies each will DECREASE to less than 15n grams.
Thus, only the ratio in Case 2 will work:
To make 10 cookies each, Micah : Jackie = 6n : 9n = 2:3.
SUFFICIENT.

Statement 2: Using his recipe, Micah requires 144 grams of sugar to make 12 cookies.
Thus, the amount of sugar in each of Micah's cookies = 144/12 = 12.
No way to determine Micah : Jackie.
INSUFFICIENT.

The correct answer is A.
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by karthikpandian19 » Thu Jul 12, 2012 9:37 pm
GMAT Guru NY.

I didnt get your method for St:1, are you assuming 10 & 15 cookies as 2 cases?
GMATGuruNY wrote:
karthikpandian19 wrote:Jackie and Micah each bake 10 cookies using two different recipes. If they use a total of 15n grams of sugar between them, what is the ratio of the amount of sugar in each of Micah's cookies to the amount of sugar in each of Jackie's cookies?

1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
Statement 1: Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
Case 1: Micah needs 9n grams to make 10 cookies, Jackie needs 9n grams make 5 cookies.
Thus, for Jackie to make 10 cookies -- twice the number of cookies here -- she will need twice the amount of sugar (18n).
Too much: 15n grams must be sufficient to make 20 cookies (10 for Micah, 10 for Jackie).

Case 2: Micah needs 9n grams to make 15 cookies, Jackie needs 9n grams to make 10 cookies.
Thus, for Micah to make 10 cookies -- 2/3 the number of cookies here -- he will need 2/3 the amount of sugar:
2/3 * 9n = 6n.
This works:
To make 10 cookies each, Micah's amount + Jackie's amount = 6n + 9n = 15n.

The progression here implies the following:
If the number of cookies INCREASES beyond the values in Case 2, the amount of sugar required by Jackie and Micah to make 10 cookies each will DECREASE to less than 15n grams.
Thus, only the ratio in Case 2 will work:
To make 10 cookies each, Micah : Jackie = 6n : 9n = 2:3.
SUFFICIENT.

Statement 2: Using his recipe, Micah requires 144 grams of sugar to make 12 cookies.
Thus, the amount of sugar in each of Micah's cookies = 144/12 = 12.
No way to determine Micah : Jackie.
INSUFFICIENT.

The correct answer is A.
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Karthik
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by GMATGuruNY » Fri Jul 13, 2012 3:39 am
karthikpandian19 wrote:GMAT Guru NY.

I didnt get your method for St:1, are you assuming 10 & 15 cookies as 2 cases?
GMATGuruNY wrote:
karthikpandian19 wrote:Jackie and Micah each bake 10 cookies using two different recipes. If they use a total of 15n grams of sugar between them, what is the ratio of the amount of sugar in each of Micah's cookies to the amount of sugar in each of Jackie's cookies?

1. Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
2. Using his recipe, Micah requires 144 grams of sugar to make 12 cookies
Statement 1: Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
Case 1: Micah needs 9n grams to make 10 cookies, Jackie needs 9n grams make 5 cookies.
Thus, for Jackie to make 10 cookies -- twice the number of cookies here -- she will need twice the amount of sugar (18n).
Too much: 15n grams must be sufficient to make 20 cookies (10 for Micah, 10 for Jackie).

Case 2: Micah needs 9n grams to make 15 cookies, Jackie needs 9n grams to make 10 cookies.
Thus, for Micah to make 10 cookies -- 2/3 the number of cookies here -- he will need 2/3 the amount of sugar:
2/3 * 9n = 6n.
This works:
To make 10 cookies each, Micah's amount + Jackie's amount = 6n + 9n = 15n.

The progression here implies the following:
If the number of cookies INCREASES beyond the values in Case 2, the amount of sugar required by Jackie and Micah to make 10 cookies each will DECREASE to less than 15n grams.
Thus, only the ratio in Case 2 will work:
To make 10 cookies each, Micah : Jackie = 6n : 9n = 2:3.
SUFFICIENT.

Statement 2: Using his recipe, Micah requires 144 grams of sugar to make 12 cookies.
Thus, the amount of sugar in each of Micah's cookies = 144/12 = 12.
No way to determine Micah : Jackie.
INSUFFICIENT.

The correct answer is A.
Using 9n grams of sugar, Micah can make 5 more cookies with his recipe than can Jackie with her recipe.
Few cases are possible here.
Using 9n grams of sugar:
Micah can make 10 cookies, Jackie can make 5 cookies.
Micah can make 11 cookies, Jackie can make 6 cookies.
Micah can make 12 cookies, Jackie can make 7 cookies.
etc.

In each of the cases above, Micah makes 5 more cookies than Jackie.
But a case is viable only if it satisfies the condition in the question stem: 15n grams of sugar must be sufficient for each to make 10 cookies.
In my solution above, I tried two cases:

Case 1: Using 9n grams of sugar, Micah can make 10 cookies, while Jackie can make 5.
Case 2: Using 9n grams of sugar, Micah can make 15 cookies, while Jackie can make 10.

Only Case 2 satisfies the condition in the question stem.
Moreover, NO OTHER CASE will satisfy the condition in the question stem.
Thus, statement 1 indicates that -- using 9n grams of sugar -- Micah can make 15 cookies, while Jackie can make 10.

Since Micah needs 9n grams to make 15 cookies, he needs 6n grams to make 10 cookies.
Thus, for each to make 10 cookies:
Micah's amount : Jackie's amount = 6n : 9n = 2:3.
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by Gaurav 2013-fall » Sat Jul 14, 2012 12:18 am
I got the answer A. Have only one doubt: How can we assume that each cookie has equal amount of sugar?
Let me tell you something you already know. The world ain't all sunshine and rainbows. It is a very mean and nasty place and it will beat you to your knees and keep you there permanently if you let it. You, me, or nobody is gonna hit as hard as life. But it ain't how hard you hit; it's about how hard you can get hit, and keep moving forward. How much you can take, and keep moving forward. That's how winning is done. Now, if you know what you're worth, then go out and get what you're worth. But you gotta be willing to take the hit, and not pointing fingers saying you ain't where you are because of him, or her, or anybody. Cowards do that and that ain't you. You're better than that! (Rocky VI)
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