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

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Verbal Forum Moderator
Status: Preparing for the another shot...!
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Kudos [?]: 772 [0], given: 62

Sammy has flavors of candies with which to make goody bags [#permalink]  16 Aug 2012, 22:53
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Difficulty:

85% (hard)

Question Stats:

43% (02:19) correct 57% (01:31) wrong based on 236 sessions
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
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 16 Aug 2012, 23:12, edited 1 time in total.
Edited the question.
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Kudos [?]: 41033 [1] , given: 5654

Re: Sammy has flavors of candies with which to make goody bags [#permalink]  16 Aug 2012, 23:32
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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).

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.

Hope it's clear.
_________________
Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1423
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 144

Kudos [?]: 772 [0], given: 62

Re: Sammy has flavors of candies with which to make goody bags [#permalink]  17 Aug 2012, 01:17
Expert's post
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?
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Kudos [?]: 41033 [0], given: 5654

Re: Sammy has flavors of candies with which to make goody bags [#permalink]  17 Aug 2012, 01:30
Expert's post
siddharthasingh wrote:
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?

This is explained here: how-many-different-5-person-teams-can-be-formed-from-a-group-96244.html#p741834 and here: how-many-different-5-person-teams-can-be-formed-from-a-group-96244.html#p742026

Similar questions to practice:
a-certain-panel-is-to-be-composed-of-exactly-three-women-and-108964.html
a-box-contains-10-light-bulbs-fewer-than-half-of-which-are-99940.html
how-many-different-5-person-teams-can-be-formed-from-a-group-96244.html

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41033 [0], given: 5654

Re: Sammy has flavors of candies with which to make goody bags [#permalink]  30 Jun 2013, 23:46
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

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Kudos [?]: 294 [0], given: 354

Re: Sammy has flavors of candies with which to make goody bags [#permalink]  29 Dec 2013, 15:35
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.

Suff

Statement 2

Rearranging x-y = 17

We have the total

Suff

Hope it helps

Cheers!
J
SVP
Joined: 06 Sep 2013
Posts: 2039
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 24

Kudos [?]: 294 [0], given: 354

Re: Sammy has flavors of candies with which to make goody bags [#permalink]  29 Mar 2014, 05:00
Bunuel 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).

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.

Hope it's clear.

Just checked suggested post on this. But still question remains. How to know that 3003 has only one solution in this question without having to solve the whole? When can we quickly spot a combinatorics with variable has one or two solutions, this is key in DS questions

Cheers
J
Re: Sammy has flavors of candies with which to make goody bags   [#permalink] 29 Mar 2014, 05:00
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