It is currently 21 Nov 2017, 21:18

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The integers n and t are positive and n > t > 1. How many

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 23 Oct 2010
Posts: 381

Kudos [?]: 403 [5], given: 73

Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

31 Mar 2012, 07:34
5
KUDOS
29
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

45% (01:12) correct 55% (01:17) wrong based on 638 sessions

### HideShow timer Statistics

The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items?

(1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680.

(2) nt = 51

good kaplan question. just wanted to share with you.
[Reveal] Spoiler: OA

_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Kudos [?]: 403 [5], given: 73

 Kaplan GMAT Prep Discount Codes e-GMAT Discount Codes Manhattan GMAT Discount Codes
Math Expert
Joined: 02 Sep 2009
Posts: 42284

Kudos [?]: 132984 [5], given: 12399

Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

31 Mar 2012, 07:49
5
KUDOS
Expert's post
13
This post was
BOOKMARKED
The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items?

The question basically asks about the value of $$C^t_n=\frac{n!}{(n-t)!*t!}$$.

(1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680 --> $$C^{n-t}_n=\frac{n!}{(n-(n-t))!*(n-t)!}=\frac{n!}{t!*(n-t)!}=680$$, directly gives us the asnwer. Sufficient.

(2) nt = 51 --> 51=17*3=51*1, since n > t > 1 then t=3 and n=17 --> $$C^t_n=\frac{n!}{(n-t)!*t!}=\frac{17!}{14!*3!}=680$$. Sufficient.

_________________

Kudos [?]: 132984 [5], given: 12399

Math Expert
Joined: 02 Sep 2009
Posts: 42284

Kudos [?]: 132984 [0], given: 12399

Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

01 Jul 2013, 00:46
Expert's post
1
This post was
BOOKMARKED
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

_________________

Kudos [?]: 132984 [0], given: 12399

Manager
Joined: 28 Feb 2012
Posts: 115

Kudos [?]: 53 [2], given: 17

Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

01 Jul 2013, 01:18
2
KUDOS
LalaB wrote:
The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items?

(1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680.

(2) nt = 51

good kaplan question. just wanted to share with you.

One of the easier ways to solve DS questions is always to look at each answer choice at glance. Just to find whether there is any idea comes to mind by looking one or another.
For example in this problem i have looked at the 1) statement and had a doubt, then i did not spend much time to solve it and moved to the 2).

2) statement tells us that these integers must be n=17 and t=3, considering the conditions of the question there are no other choices. So we can solve this problem. Although we do not need to it i will solve it: we are looking for how many groups of 3 integers we can form out of 17 (considering that 1 would not make any difference i am saying 17).
(17*16*15)/3*2=680

By looking at this answer choice we can state that it is the same as the answer which is given in the statement (1). You can try couple of different values to get the combination of 680, but i am more than sure that you will not be able to get such combination without using 17 and 3.
So i am concluding that the answer is D.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Kudos [?]: 53 [2], given: 17

Non-Human User
Joined: 09 Sep 2013
Posts: 15577

Kudos [?]: 283 [0], given: 0

Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

23 Jul 2014, 08:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15577

Kudos [?]: 283 [0], given: 0

Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

24 Jul 2015, 04:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15577

Kudos [?]: 283 [0], given: 0

Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

14 Aug 2016, 09:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Intern
Joined: 05 Feb 2014
Posts: 16

Kudos [?]: [0], given: 18

Location: India
Concentration: Human Resources, General Management
Schools: Tepper '20 (S)
GMAT 1: 720 Q49 V40
GPA: 3.33
Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

14 Sep 2016, 07:22
Bunuel wrote:
The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items?

The question basically asks about the value of $$C^t_n=\frac{n!}{(n-t)!*t!}$$.

(1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680 --> $$C^{n-t}_n=\frac{n!}{(n-(n-t))!*(n-t)!}=\frac{n!}{t!*(n-t)!}=680$$, directly gives us the asnwer. Sufficient.

(2) nt = 51 --> 51=17*3=51*1, since n > t > 1 then t=3 and n=17 --> $$C^t_n=\frac{n!}{(n-t)!*t!}=\frac{17!}{14!*3!}=680$$. Sufficient.

Hi Bunnuel

Can we consider this as a ratio problem where we are asked to find the ratio of n to t. Even by this logic both the statements are enough!!

Kudos [?]: [0], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 42284

Kudos [?]: 132984 [0], given: 12399

Re: The integers n and t are positive and n > t > 1. How many [#permalink]

### Show Tags

14 Sep 2016, 08:19
SunthoshiTejaswi wrote:
Bunuel wrote:
The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items?

The question basically asks about the value of $$C^t_n=\frac{n!}{(n-t)!*t!}$$.

(1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680 --> $$C^{n-t}_n=\frac{n!}{(n-(n-t))!*(n-t)!}=\frac{n!}{t!*(n-t)!}=680$$, directly gives us the asnwer. Sufficient.

(2) nt = 51 --> 51=17*3=51*1, since n > t > 1 then t=3 and n=17 --> $$C^t_n=\frac{n!}{(n-t)!*t!}=\frac{17!}{14!*3!}=680$$. Sufficient.

Hi Bunnuel

Can we consider this as a ratio problem where we are asked to find the ratio of n to t. Even by this logic both the statements are enough!!

Just knowing the ratio won't be enough. For example, knowing that n/t = 3/2, won't be enough to answer the question.
_________________

Kudos [?]: 132984 [0], given: 12399

Re: The integers n and t are positive and n > t > 1. How many   [#permalink] 14 Sep 2016, 08:19
Display posts from previous: Sort by

# The integers n and t are positive and n > t > 1. How many

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.