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

It is currently 26 Mar 2019, 01:41

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In a box there are 4 ball point pens, and 3 fountain pens. How many

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

Hide Tags

 
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2722
In a box there are 4 ball point pens, and 3 fountain pens. How many  [#permalink]

Show Tags

New post 29 May 2018, 01:59
1
1
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:29) correct 34% (02:50) wrong based on 53 sessions

HideShow timer Statistics

In a box there are 4 ball point pens, and 3 fountain pens. How many possible selections can be formed which have at least 2 items of every types of pen?

    A. 26
    B. 44
    C. 52
    D. 78
    E. 130



To solve question 2: P&C Practice Question 2

Related Articles:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions
Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
Article-3: 3 deadly mistakes you must avoid in Permutation & Combination

All Articles: Must Read Articles and Practice Questions to score Q51 !!!!

_________________







Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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 | Inequalities

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

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3365
Location: India
GPA: 3.12
Premium Member
In a box there are 4 ball point pens, and 3 fountain pens. How many  [#permalink]

Show Tags

New post 29 May 2018, 02:55
1
EgmatQuantExpert wrote:
In a box there are 4 ball point pens, and 3 fountain pens. How many possible selections can be formed which have at least 2 items of every types of pen?

    A. 26
    B. 44
    C. 52
    D. 78
    E. 130



When we need a minimum of 2 pens of each type, these are the following options available:

When we have 2 ball-point pens
1. Along with 2 fountain pens - \(C_2^4 * C_2^3 = 6*3 = 18\)
2. Along with 3 fountain pens - \(C_2^4 * C_3^3 = 6*1 = 6\)

When we have 2 fountain pens
1. Along with 3 ball-point pens - \(C_2^3 * C_3^4 = 3*4 = 12\)
2. Along with 4 ball-point pens - \(C_2^3 * C_4^4 = 3*1 = 3\)

When we have 3 ball-point pens along with 3 fountain pens - \(C_3^3 * C_3^4 = 1*4 = 4\)

When we have all 7 pens - \(C_3^3 * C_4^4 = 1*1 = 1\)

The total possibilities are 18 + 6 + 12 + 3 + 4 + 1 = 44

Therefore, there are 44(Option B) possible selections which have at least 2 items of every types of pen.
_________________
You've got what it takes, but it will take everything you've got
Intern
Intern
avatar
B
Joined: 21 Apr 2018
Posts: 2
Re: In a box there are 4 ball point pens, and 3 fountain pens. How many  [#permalink]

Show Tags

New post 29 May 2018, 04:25
answer must be 44 as it is "or" question
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2722
Re: In a box there are 4 ball point pens, and 3 fountain pens. How many  [#permalink]

Show Tags

New post 31 May 2018, 02:03

Solution



Given:
    • In the box,
      o Ball point pens = 4
      o Fountain pens = 3

To find:
    • How many possible selections can be formed which have at least 2 items of every types of pen

Approach and Working:
As we have to ensure at least 2 items of every types of pen, the different possible cases and their respective possibilities are as follows:
    • 2 ball point pens and 2 fountain pens = \(^4C_2 * ^3C_2 = 6 * 3 = 18\)
    • 3 ball point pens and 2 fountain pens = \(^4C_3 * ^3C_2 = 4 * 3 = 12\)
    • 4 ball point pens and 2 fountain pens = \(^4C_4 * ^3C_2 = 1 * 3 = 3\)
    • 2 ball point pens and 3 fountain pens = \(^4C_2 * ^3C_3 = 6 * 1 = 6\)
    • 3 ball point pens and 3 fountain pens = \(^4C_3 * ^3C_3 = 4 * 1 = 4\)
    • 4 ball point pens and 3 fountain pens = \(^4C_4 * ^3C_3 = 1 * 1 = 1\)

Therefore, total number of possible selections = 18 + 12 + 3 + 6 + 4 + 1 = 44

Hence, the correct answer is option B.

Answer: B
_________________







Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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 | Inequalities

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

Manager
Manager
User avatar
S
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 141
Re: In a box there are 4 ball point pens, and 3 fountain pens. How many  [#permalink]

Show Tags

New post 16 Feb 2019, 10:14
The question is asking for the #ways to choose at least 2 b and f pens

For b: For f:
4C0=1, 3C0=1
4C1=4, 3C1=3

4C2=6, 3C2=3
4C3=4, 3C1=1
4C4=1
+ =11,+ = 4

11 ways to chose b*4 ways to choose f = 44
GMAT Club Bot
Re: In a box there are 4 ball point pens, and 3 fountain pens. How many   [#permalink] 16 Feb 2019, 10:14
Display posts from previous: Sort by

In a box there are 4 ball point pens, and 3 fountain pens. How many

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.