In a certain mathematical activity, we start with seven...

Expert replies

BTGmoderatorLU: Moderator; Posts: 2611; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Dec 29, 2017 6:17 am

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 fours 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

The OA is B.

I'm really confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

Like this post

Source: Beat The GMAT — Problem Solving | Fri Dec 29, 2017 6:17 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Fri Dec 29, 2017 11:32 am

LUANDATO wrote: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 fours 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

The OA is B.

I'm really confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

Box #1 (four cards) We've got 7 numbers to select from. We want to select 4 of them. So we want 7C4 = 7*6*5*4/4*3*2*1 = 35 options for the first box.

Box #2 (two cards). If we started with 7 numbers, and we've selected 4, we only have 3 cards remaining. Of these 3, we want to select 2, so we want 3C2 = 3*2/2*1 = 3 options for the second box.

Box #3 (one card). We started with 7 numbers. We selected 4 for the first box and 2 for the second box, so there's only one number left. That would leave us 1 lonely option for the last box.

Multiply the results: 35 * 3 * 1 = 105. The answer is B

Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review