Last visit was: 27 Mar 2025, 13:25 It is currently 27 Mar 2025, 13:25
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 March 2025
Posts: 100,114
Own Kudos:
Given Kudos: 92,732
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,114
Kudos: 711,377
 [23]
3
Kudos
Add Kudos
20
Bookmarks
Bookmark this Post
User avatar
Lucky2783
Joined: 07 Aug 2011
Last visit: 08 May 2020
Posts: 419
Own Kudos:
1,939
 [4]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT 1: 630 Q49 V27
Posts: 419
Kudos: 1,939
 [4]
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
peachfuzz
Joined: 28 Feb 2014
Last visit: 27 Jan 2018
Posts: 269
Own Kudos:
345
 [3]
Given Kudos: 132
Location: United States
Concentration: Strategy, General Management
Products:
Posts: 269
Kudos: 345
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
neerajsubhedar
Joined: 08 Oct 2014
Last visit: 27 Jun 2015
Posts: 2
Own Kudos:
7
 [1]
Given Kudos: 19
GPA: 3.24
Posts: 2
Kudos: 7
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets can be created from this process?

(A) 35
(B) 105
(C) 210
(D) 420
(E) 630


Kudos for a correct solution.

Answer should be (B) 105

7! / 4! 2! 1!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 March 2025
Posts: 100,114
Own Kudos:
711,377
 [3]
Given Kudos: 92,732
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,114
Kudos: 711,377
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets can be created from this process?

(A) 35
(B) 105
(C) 210
(D) 420
(E) 630


Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Part of the logic of the problem involves recognizing that every unique combination of prime numbers produces a unique product. There is no way that two different groupings cards will produce the same set of numbers.

First of all, the cards to go into the cup holding 4 cards.

7C4 = 35.

Once we have placed 4 card in the first cup, we have three cards left, which means we have three choices of a single card to put into the third cup. Three choices. Once we place that, the remaining two cards must go into the second cup: no choice there.

N = 35*3 = 105

Answer = (B)
User avatar
rhine29388
Joined: 24 Nov 2015
Last visit: 21 Oct 2019
Posts: 401
Own Kudos:
133
 [1]
Given Kudos: 231
Location: United States (LA)
Products:
Posts: 401
Kudos: 133
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
7C4 *3C2 = 35 *3 = 105
correct answer option B
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,716
Own Kudos:
Posts: 36,716
Kudos: 963
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
100114 posts
PS Forum Moderator
518 posts