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

It is currently 20 Feb 2019, 15:53

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

Combinatorics example question (Two methods..different results)

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

Hide Tags

 
Intern
Intern
avatar
B
Joined: 24 Apr 2017
Posts: 13
Combinatorics example question (Two methods..different results)  [#permalink]

Show Tags

New post 25 Jan 2019, 00:35
Hi Team,
I'm reviewing combinators questions. I came to a question that I solved my way and the book solved it another way.

The question is (I changed the names and items a bit):
John is maxing boxes of grapes to give to his friends. He has unlimited supply of 5 different grape colors. If each box has 2 grapes of different colors, how many boxes can he make?

I answered the following:
First grape has 5 options. Second grade has 4 options. In total 5*4 = 20.

Another solution (correct one) for the problem is by anagram YYNNN = 5!/(2!3!)=10



Question 1: So my question is when to answer using the first method and when by the second method?
Question 2: The two solutions differ by a factor of 2. If numbers of grapes in the box change from 2 to 3, the solution will differ by a factor of 6! What's the catch?
Thank you
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: Combinatorics example question (Two methods..different results)  [#permalink]

Show Tags

New post 25 Jan 2019, 18:22
mekhdi wrote:
Hi Team,
I'm reviewing combinators questions. I came to a question that I solved my way and the book solved it another way.

The question is (I changed the names and items a bit):
John is maxing boxes of grapes to give to his friends. He has unlimited supply of 5 different grape colors. If each box has 2 grapes of different colors, how many boxes can he make?

I answered the following:
First grape has 5 options. Second grade has 4 options. In total 5*4 = 20.

Another solution (correct one) for the problem is by anagram YYNNN = 5!/(2!3!)=10



Question 1: So my question is when to answer using the first method and when by the second method?
Question 2: The two solutions differ by a factor of 2. If numbers of grapes in the box change from 2 to 3, the solution will differ by a factor of 6! What's the catch?
Thank you


Hi..

The two methods you talk of..
(1) 5*4 is nothing but 5P2 or 5C2*2!. So this method talks of ways where order matters and us a Permutation problem. Will work where you have to pick two person out of 5 for post of president and vice President.
But not here, because this is selection of two types of grapes and not arrangements of 2 types of grapes.
So this is wrong.
(2) 5/3!2! Is a combination problem that is ways where order does not matter and is correct here.

Hope it helps clarifying your query
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 689
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Combinatorics example question (Two methods..different results)  [#permalink]

Show Tags

New post 26 Jan 2019, 13:33
mekhdi wrote:
Hi Team,
I'm reviewing combinators questions. I came to a question that I solved my way and the book solved it another way.

The question is (I changed the names and items a bit):
John is maxing boxes of grapes to give to his friends. He has unlimited supply of 5 different grape colors. If each box has 2 grapes of different colors, how many boxes can he make?

I answered the following:
First grape has 5 options. Second grade has 4 options. In total 5*4 = 20.

Another solution (correct one) for the problem is by anagram YYNNN = 5!/(2!3!)=10



Question 1: So my question is when to answer using the first method and when by the second method?
Question 2: The two solutions differ by a factor of 2. If numbers of grapes in the box change from 2 to 3, the solution will differ by a factor of 6! What's the catch?
Thank you


When you solved the problem the first way, you actually counted all of the boxes twice. To see why, try calling the grapes A, B, C, D, and E. Here are the '5 times 4' options:

A (B, C, D, E)
B (A, C, D, E)
C (A, B, D, E)
D (A, B, C, E)
E (A, B, C, D)

For instance, the first line represents the options AB, AC, AD, AE; the second line represents the options BA, BC, BD, BE; etc.

But, look at that again. We counted AB, and we also counted BA separately. We counted AC (on the first line), but we also counted CA. And so on. You don't actually want to count those options twice, because those aren't actually unique boxes: a box with A and B is the same as a box with B and A.

That's why you need to divide your answer by 2 when you approach it this way: to compensate for the fact that you counted every option twice, instead of just once.
_________________

Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!

GMAT Club Bot
Re: Combinatorics example question (Two methods..different results)   [#permalink] 26 Jan 2019, 13:33
Display posts from previous: Sort by

Combinatorics example question (Two methods..different results)

  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®.