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

Redeem

greatest common divisor of positive integers m and n

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
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
Top
User avatar
Legendary Member
Posts: 2135
Joined: Mon Feb 03, 2014 9:26 am
Location: https://martymurraycoaching.com/
Thanked: 955 times
Followed by:140 members
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.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

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]

Image

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
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
Image
Top
Post new topic Post Reply
• Page 1 of 1