GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2018, 15:45

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1251
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

Updated on: 17 Aug 2012, 00:12
4
1
28
00:00

Difficulty:

95% (hard)

Question Stats:

47% (01:23) correct 53% (01:38) wrong based on 699 sessions

### HideShow timer Statistics

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

_________________

Originally posted by Marcab on 16 Aug 2012, 23:53.
Last edited by Bunuel on 17 Aug 2012, 00:12, edited 1 time in total.
Edited the question.
 Jamboree Discount Codes Veritas Prep GMAT Discount Codes Kaplan GMAT Prep Discount Codes
Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

17 Aug 2012, 00:32
8
13
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.
_________________
##### General Discussion
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1251
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

17 Aug 2012, 02:17
1
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?
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

17 Aug 2012, 02:30
1
1
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: 48067
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

01 Jul 2013, 00:46
1
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

_________________
SVP
Joined: 06 Sep 2013
Posts: 1850
Concentration: Finance
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

29 Dec 2013, 16:35
1
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
Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

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...
Intern
Joined: 04 Jan 2016
Posts: 1
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

15 Jul 2016, 10:44
Can anyone help how to solve the combination:
(x-y-2)C10=3003
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3186
Location: United States (CA)
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

30 Jul 2017, 17:48
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

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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 01 Jul 2018
Posts: 8
Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

10 Jul 2018, 05:32
How do you make sure that it has only one solution without solving it, did we just assume it?

It may have 10 different roots. (let's say x-y-2 is a) C(a, 10) = ((a).(a-1).(a-2)....(a-9))/10!=3003

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.
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1343
Location: India
Re: Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

10 Jul 2018, 22:16
[quote="financestudent"]How do you make sure that it has only one solution without solving it, did we just assume it?

It may have 10 different roots. (let's say x-y-2 is a) C(a, 10) = ((a).(a-1).(a-2)....(a-9))/10!=3003

Hello

You are right that we can simplify this as: ((a).(a-1).(a-2)....(a-9))/10!=3003
We can say that ((a).(a-1).(a-2)....(a-9)) = 3003*10!

Now since 3003*10! is a unique number (no matter how big it is), there can be ONLY single value of a positive integer 'a' such that ((a).(a-1).(a-2)....(a-9)) equals 3003*10!. Since this is data sufficiency, we dont need to find the value of 'a'. If we know for sure that a unique value of 'a' exists, the statement is sufficient.
Intern
Joined: 01 Jul 2018
Posts: 8
Sammy has flavors of candies with which to make goody bags  [#permalink]

### Show Tags

11 Jul 2018, 00:35
Hi there, thank you for the explanation.

Can you also explain how you figured out that 3003*10! is a unique number or how can I tell that a number is unique (especially like this big one)?

Bunuel amanvermagmat

amanvermagmat wrote:
financestudent wrote:
How do you make sure that it has only one solution without solving it, did we just assume it?

It may have 10 different roots. (let's say x-y-2 is a) C(a, 10) = ((a).(a-1).(a-2)....(a-9))/10!=3003

Hello

You are right that we can simplify this as: ((a).(a-1).(a-2)....(a-9))/10!=3003
We can say that ((a).(a-1).(a-2)....(a-9)) = 3003*10!

Now since 3003*10! is a unique number (no matter how big it is), there can be ONLY single value of a positive integer 'a' such that ((a).(a-1).(a-2)....(a-9)) equals 3003*10!. Since this is data sufficiency, we dont need to find the value of 'a'. If we know for sure that a unique value of 'a' exists, the statement is sufficient.
Sammy has flavors of candies with which to make goody bags &nbs [#permalink] 11 Jul 2018, 00:35
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.