For a fundraising dinner, a florist is asked to create

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Tue Oct 14, 2014 8:23 am
Thanked: 1 times
For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
4
5
6
7
8

OAA

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Mar 25, 2015 10:23 am
gmat_winter wrote:For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
4
5
6
7
8
Each of the 8 tables is to receive either 1 type of flower or 3 types of flower.
We can PLUG IN THE ANSWERS, which represent the least number of flower types needed.
When the correct answer choice is plugged in, at least 8 different bouquets will be possible.
Since we must determine the LEAST number of flower types needed, we should test the SMALLEST answer choice first.

Answer choice A: 4
Let the 4 types of flowers be A, B, C and D.
Bouquet options:
A
B
C
D
ABC
ABD
ACD
BCD
Total options = 8.
Success!

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Mar 25, 2015 6:04 pm
Hi gmat_winter,

Mitch's approach (TESTing THE ANSWERS) is a great way to tackle this type of question. You can also solve it using the Combination Formula and doing a bit of math.

Combinations = N!/K!(N-K)! Where N is the total number of items and K is the number of items in the 'subgroup'

The question asks to form 8 different flower bouquets using groups of flowers. We can make a bouquet with just 1 type of flower or 3 different types of flowers. We're asked for the LEAST number of different types of flowers needed to create 8 different bouquets.

Let's start with the SMALLEST Answer.

With 4 different types of flower, we could have....

Bouquets with just 1 flower = 4c1 = 4!/(1!3!) = 4 different options

Bouquets with 3 different flowers = 4c3 = 4!/(3!1!) = 4 different options

Here, we have 4+4 = 8 different options, which is exactly what we're looking for. This MUST be the answer.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image