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Sammy has flavors of candies with which to make goody bags [#permalink]

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16 Aug 2012, 23:53

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A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

44% (01:18) correct
56% (01:39) wrong based on 663 sessions

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Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

In order to calculate how many 10-flavor bags can Sammy make from the remaining (x-y) flavors, we should know the value of x-y. The answer would simply be \(C^{10}_{x-y}\). For example if he has 11 flavors (if x-y=11), then he can make \(C^{10}_{11}=11\) different 10-flavor bags.

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. We are told that \(C^{10}_n=3,003\), where \(n=(x-y)-2\): he can make 3,003 10-flavor bags out of n flavors. Now, n can take only one particular value, so we can find n (it really doesn't matter what is the value n, important is that we can find it), hence we can find the value of x-y (x-y=n+2). Sufficient.

(2) x = y + 17 --> x-y=17. Directly gives us the value of x-y. Sufficient.

Re: Sammy has flavors of candies with which to make goody bags [#permalink]

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17 Aug 2012, 02:17

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Hey thanx. But I shall like to bother you again. I have come across around 3 questions of this type where the value of the total, of which we are supposed to make selection, is not known. Even in this question also, I knew that there could be only one value for which the answer comes out to be 3003, but since I was unable to come out with the solution, I sought help. So my question is that can't there be any more value for n for which nC10 is 3003?
_________________

Hey thanx. But I shall like to bother you again. I have come across around 3 questions of this type where the value of the total, of which we are supposed to make selection, is not known. Even in this question also, I knew that there could be only one value for which the answer comes out to be 3003, but since I was unable to come out with the solution, I sought help. So my question is that can't there be any more value for n for which nC10 is 3003?

Re: Sammy has flavors of candies with which to make goody bags [#permalink]

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29 Dec 2013, 16:35

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Marcab wrote:

Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

Source-jamboree

OK, let me try this one

Question stem basically says we have x-y flavors and we need to pick 10 out of these

How many combinations can we make?

Statement 1

So this is giving us the number of combinations of x-y-2, therefore we can imply what x-y is. Do we need the calculation? No, there will only be one number that will give this answer when deciding to pick 10 out of it.

Re: Sammy has flavors of candies with which to make goody bags [#permalink]

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08 Mar 2016, 19:19

I was concerned more with finding the value of y..but looks like it was not really necessary... how i approached the question: 1. (x-y-2)C10 = 3003 -> find prime factorization of 3003...we can see that we have 3*7*11*13... (x-y-2)x(x-y-1)x(x-y)(x-y+1) x etc. / 10!*(x-y-12)!

how can we solve further???

2. x-y=17 17C10 - we can find the answer... so somewhere I did not see how to solve A...

Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

We need to determine the number of different 10-flavor goody bags Sammy can make for Frank. Since there were x flavors to begin with and y were thrown away, there are (x - y) remaining flavors. Moreover, since the order in which the flavors are chosen is not important, this is a combination problem. In other words, we must determine whether we have enough information to calculate (x - y)C10.

Statement One Alone:

If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags.

This statement tells us that (x - y b- 2)C10 = 3003. The important thing to remember when approaching questions like this is that we don’t actually need to find the answer; we simply need to determine whether we have enough information to answer the question. In this case, since there is a unique value for (x - y - 2) that satisfies (x - y - 2)C10 = (x - y - 2)!/((x - y - 12)! * 10!), we can determine (x - y - 2), and thus we can determine x - y. After x - y is determined, it is easy to calculate (x - y)C10.

Statement one alone provides enough information to answer the question.

Statement Two Alone:

x = y + 17

We have x - y = 17; thus, 17C10 = 17!/(7! * 10!) can be calculated.

Statement two alone provides enough information to answer the question.

Answer: D
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