For positive integers n and m, is m! < 3^n ?

Expert replies

BTGmoderatorLU: Moderator; Posts: 2550; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Oct 28, 2017 7:55 am

For positive integers n and m, is m! < 3^n ?

(1) n = m

(2) n > 3

The OA is E.

I don't understand this DS question. Can any expert explain it for me please? Thanks.

Like this post

Source: Beat The GMAT — Data Sufficiency | Sat Oct 28, 2017 7:55 am

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Oct 30, 2017 3:22 am

LUANDATO wrote:For positive integers n and m, is m! < 3^n ?

(1) n = m
(2) n > 3

The OA is E.

I don't understand this DS question. Can any expert explain it for me please? Thanks.

(1) n = m

Certainly insufficient.

Case 1: Say n = m = 1, then m! = 1! = 1 and 3^n = 3^1 = 3. The answer is Yes.
Case 2: Say n = m = 6, then m! = 7! = 1.2.3.4.5.6.7 = 720.7 and 3^n = 3^6 = 3.3.3.3.3.3.3 = 729.3. We see that 720.7 > 729.3. The answer is No.

(2) n > 3

We hve seen Case 2: Say n = m = 6, then m! = 7! = 1.2.3.4.5.6.7 = 720.7 and 3^n = 3^6 = 3.3.3.3.3.3.3 = 729.3. The answer is No.

Case 3: Say n = m = 4, then m! = 7! = 1.2.3.4. = 24 and 3^n = 3^4 = 3.3.3.3 = 81. The answer is Yes. No uniqe answer.

(1) and (2) combined:

Case 2 and Case 3 are applicable here too. Thus, there is no unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
_________________
Manhattan Review GMAT Prep

Locations: New York | New Delhi | Seoul | Cairo | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 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