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

 It is currently 20 Aug 2018, 02:07

### 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

# There were n boys and m girls in a class.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 12 Jun 2017
Posts: 7
GMAT 1: 710 Q49 V38
There were n boys and m girls in a class.  [#permalink]

### Show Tags

18 Jun 2018, 10:13
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:18) correct 44% (01:30) wrong based on 75 sessions

### HideShow timer Statistics

There were n boys and m girls in a class. They wanted to sit in a row for an activity. In how many ways can they sit on 30 chairs?
I. n+3m = 20
II. 2n + 2m = 22
DS Forum Moderator
Joined: 27 Oct 2017
Posts: 675
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: There were n boys and m girls in a class.  [#permalink]

### Show Tags

18 Jun 2018, 10:29
There were n boys and m girls in a class. They wanted to sit in a row for an activity. In how many ways can they sit on 30 chairs?
To find the number of ways , we need the total number of students.
If N is total number of students, Number of ways will be $$30CN *N!$$

I. n+3m = 20
Value of (n, m) can be (2,6) or (5,5) or (8,4)
So N = n+m= 8 or 10 or 12.
NOT SUFFICIENT.

II. 2n + 2m = 22
N= n+m = 11
SUFFICIENT.

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1900
Re: There were n boys and m girls in a class.  [#permalink]

### Show Tags

18 Jun 2018, 23:44

Solution

Given:
• There were n boys and m girls in a class – they wanted to sit in a row for an activity

To find:
• The number of ways n boys and m girls can sit on 30 chairs

Approach and Working:
We have total 30 chairs available, and there is (n + m) number of people to sit in those 30 chairs

Assuming that (n + m) is less than or equal to 30,
• The number of ways they can sit in 30 chairs = $$^{30}P_{n+m}$$

Hence, if we know the value of (n + m), we can answer the question

Analysing Statement 1
• As per the information given in statement 1, n + 3m = 20
o From this equation, we can’t find the value of n + m

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in statement 2, 2n + 2m = 22
o Or, we can write, n + m = 11

• Replacing the value of (n + m), we can find out the value of $$^{30}P_{n+m}$$

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Joined: 02 Nov 2017
Posts: 22
Location: India
Concentration: General Management, Finance
Schools: ISB
GMAT 1: 690 Q50 V35
GPA: 3.31
WE: General Management (Energy and Utilities)
Re: There were n boys and m girls in a class.  [#permalink]

### Show Tags

16 Jul 2018, 06:44
DarshilPandya wrote:
There were n boys and m girls in a class. They wanted to sit in a row for an activity. In how many ways can they sit on 30 chairs?
I. n+3m = 20
II. 2n + 2m = 22

SInce Obviously boys and girls are different....final result is 30/((n+m)! (30-n-m)!) x 11!/(n! x m!).....since values of n and m are not known....(B) is also not sufficient.

(C) doesn't give values of n and m...so answer should be (E).

Had the question asked what the number of ways of selecting chairs for total students...n+m would have been sufficient to answer the question.

Ways of sitting ...it means no. of ways of selecting chairs x no of arrangements of boys and girls.

ANS (E)
Re: There were n boys and m girls in a class. &nbs [#permalink] 16 Jul 2018, 06:44
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®.