Suppose we have six marbles: 3 blue marbles, 2 red marbles,

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

Suppose we have six marbles: 3 blue marbles, 2 red marbles,

by AAPL » Thu Jan 31, 2019 5:05 am

Timer

00:00

Your Answer

Global Stats

Magoosh

Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can't be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don't involve the two red marbles in the same cup. How many combinations are possible?

A. 90
B. 180
C. 360
D. 540
E. 720

OA A

Quote

Source: Beat The GMAT — Problem Solving | Thu Jan 31, 2019 5:05 am

GMAT/MBA Expert

[email protected]: 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] » Thu Jan 31, 2019 2:15 pm

Hi All,

We're told that we have six marbles: 3 blue marbles, 2 red marbles, and one green marble - and that we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles CANNOT be in the same cup, meaning that we could put as many as five (all except one of the reds) in any one cup. We could leave one cup empty, or put some in each of the three cups. We're asked for the number of possible combinations. While this question might appear complex, by breaking it down into 'pieces', the individual math steps aren't too difficult.

Let's start with the green marble. It can be in any of the 3 distinct cups, so there are 3 possible placements for that marble.

Next, we know that the two red marbles CANNOT be in the same cup. If we call the cups A, B and C, then the two red marbles could be in 3 possible placements:
A&B
A&C
B&C
Thus, there are 3 possibilities for the reds

The 3 blues provide the largest number of different options. Listing them out won't be difficult though. Across the 3 cups, the 3 blues could be:
0, 0, 3
0, 3, 0
3, 0, 0
1, 1, 1
0, 1, 2
0, 2, 1
1, 0, 2
1, 2, 0
2, 0, 1
2, 1, 0
Thus, there are 10 possibilities for the blues.

Total possible arrangements = (3)(3)(10) = 90

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]