greatest common divisor of positive integers m and n

Expert replies

jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Fri May 06, 2016 9:48 pm

What is the greatest common divisor of positive integers m and n ?

1) m is a prime number

2) 2n = 7m

OAC

Hi Experts ,

Please explain.

Many thanks in advance.

SJ

Like this post

Source: Beat The GMAT — Data Sufficiency | Fri May 06, 2016 9:48 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri May 06, 2016 9:51 pm

What is the greatest common divisor of positive integers m and n?

1) m is a prime number
2) 2n = 7m

Statement 1 is clearly INSUFFICIENT.
When one of the statements is clearly insufficient, consider how it might affect the OTHER statement.
Since statement 1 is in terms of m, rephrase statement 2 in terms of m.

Statement 2: m = (2/7)n
The smallest possible value for n is 7.

Case 1: n=7, m = (2/7)(7) = 2.
The GCF of 2 and 7 is 1.

Case 2: n=14, m=(2/7)(14) = 4.
The GCF of 4 and 14 is 2.

Since the GCF can be different values, INSUFFICIENT.

Statements combined:
Cases 1 and 2 imply that m must be EVEN.
One more case to confirm:

Case 3: n=21, m = (2/7)(21) = 6.
Case 3 confirms that m must be even.

Since statement 1 indicates that m is prime, only Case 1 -- m=2, n=7 -- satisfies both statements.
In Case 1, the GCF m and n is 1.
SUFFICIENT.

The correct answer is C.

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

Like this post

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Fri May 06, 2016 10:24 pm

jain2016 wrote:What is the greatest common divisor of positive integers m and n ?

1) m is a prime number

2) 2n = 7m

Statement 1: m is a prime number

Since m could be any prime number and n could be equal to m, there are many possible answers that satisfy Statement 1.

Insufficient.

Statement 2: 2n = 7m

Since n and m are integers, this statement implies that 7 is a factor of n and 2 is a factor of m, and that other than 7 and 2, the factors of n and m are the same.

In other words, n/m = 7/2, n:m = 7:2, and n = 7k and m = 2k.

For instance, n could be 7 x 5 x 11 and m could be 2 x 5 x 11, in which case their greatest common divisor would be 55.

Alternatively n could be 7 x 1 and m could be 2 x 1, in which case their greatest common divisor would be 1.

Insufficient.

Statements Combined:

There is only one number that is both prime and a multiple of 2. So m = 2 and n = 7, and the greatest common divisor of n and m is 1.

Sufficient.

The correct answer is C.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Dec 19, 2017 9:26 am

jain2016 wrote:What is the greatest common divisor of positive integers m and n ?

1) m is a prime number

2) 2n = 7m

We need to determine the greatest common divisor, or the greatest common factor (GCF), of integers m and n.

Statement One Alone:

m is a prime number.

Since we don't know anything about n, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

2n = 7m

We can manipulate the equation 2n = 7m:

n = 7m/2

n/m = 7/2

Even with the equation rewritten, we see that there are many options for m and n, and thus there are many different GCFs for m and n. For instance, if n = 7 and m = 2, then the GCF is 1. However, if n = 14 and m = 4, then the GCF is 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that m is prime and that n/m = 7/2. Therefore, m must equal 2 and n must equal 7. When m is 2 and n is 7, the GCF is 1.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 22, 2017 10:52 am

jain2016 wrote:What is the greatest common divisor of positive integers m and n ?

1) m is a prime number

2) 2n = 7m

Target question: What is the GCD of m and n?

Statement 1: m is a prime number
If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the GCD of m and n must be either 1 or m.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT.

Statement 2: 2n = 7m
If 2n = 7m then we can rearrange the equation to get n = (7/2)m

IMPORTANT: Notice that if m were to equal an ODD number, then n would not be an integer. For example, if m = 3, then n = 21/2 (n is not an integer). Similarly, if m = 11, then n = 77/2 (n is not an integer). So, in order for n to be an INTEGER, m must be EVEN.

If m must be EVEN, there are several possible values for m and n. Consider these two cases:
case a: m = 2 and n = 7, in which case the GCD = 1
case b: m = 4 and n = 14, in which case the GCD=2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT.

Statements 1 & 2 combined
From statement 1, we know that m is prime, and from statement 2, we know that m is even.
Since 2 is the only even prime number, we can conclude that m must equal 2.
If m = 2, then n must equal 7, which means that the GCD must be 1.
Since we are able to answer the target question with certainty, statements 1 & 2 combined are sufficient, and the answer is C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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