GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 08:58

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If GCD of two numbers (both integers, greater than 1) is 1, then whic

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 13 Jun 2013
Posts: 266
If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

19 Nov 2014, 01:47
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:29) correct 43% (01:22) wrong based on 84 sessions

### HideShow timer Statistics

If GCD of two numbers (both integers, greater than 1) is 1, then which of the following must be true?

1. They are prime.
2. They are consecutive.
3. They do not have a common prime factor
4. They do not have a common factor other than 1

I. Only 1
II. Only 2
III. Only 3 and 4
IV. Only 1 and 4
V. 1, 2, 3 and 4
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

19 Nov 2014, 02:16
manpreetsingh86 wrote:
If GCD of two numbers (both integers, greater than 1) is 1, then which of the following must be true?
1. They are prime.
2. They are consecutive.
3. They do not have a common prime factor
4. They do not have a common factor other than 1

I. Only 1
II. Only 2
III. Only 3 and 4
IV. Only 1 and 4
V. 1, 2, 3 and 4

Is the OA correct??

I get the answer 2,3 & 4

Are these (including the others) GMAT questions?
_________________
Kindly press "+1 Kudos" to appreciate
Senior Manager
Joined: 13 Jun 2013
Posts: 266
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

19 Nov 2014, 02:25
PareshGmat wrote:
manpreetsingh86 wrote:
If GCD of two numbers (both integers, greater than 1) is 1, then which of the following must be true?
1. They are prime.
2. They are consecutive.
3. They do not have a common prime factor
4. They do not have a common factor other than 1

I. Only 1
II. Only 2
III. Only 3 and 4
IV. Only 1 and 4
V. 1, 2, 3 and 4

Is the OA correct??

I get the answer 2,3 & 4

Are these (including the others) GMAT questions?

yes, they all are gmat questions. concepts tested in these questions are quite often tested in real gmat. As per your doubt, consider two number as 2,5 gcd is 1, but they are not consecutive. now consider 3,4 they are consecutive and gcd is 1. now since, this is a must be true kind of question. therefore, correct answer must be true under all the conditions. hence two is incorrect.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

19 Nov 2014, 02:41
ok fine; seems I got confused in between solving it.......
_________________
Kindly press "+1 Kudos" to appreciate
Manager
Joined: 21 Sep 2012
Posts: 208
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

19 Nov 2014, 08:40
1
Ans has to be C.

15,16 are not prime numbers, but GCD for them is 1. so statement one is incorrect.
2,7 have 1 as GCD, but they are not consecutive numbers.
Statement 3 and 4 are correct. Since GCD is 1, we can't have a common prime factor or a common factor other than 1 for the two numbers.

Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

21 Nov 2014, 07:32
manpreetsingh86 wrote:
If GCD of two numbers (both integers, greater than 1) is 1, then which of the following must be true?

1. They are prime.
2. They are consecutive.
3. They do not have a common prime factor
4. They do not have a common factor other than 1

I. Only 1
II. Only 2
III. Only 3 and 4
IV. Only 1 and 4
V. 1, 2, 3 and 4

The above is a concept on properties of Co-prime Numbers

Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1.

Numbers that can be Co-Prime are :

(a) Two consecutive natural numbers.
(b) Two consecutive odd numbers.
(c) Two prime numbers.
(d) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.

Now analyzing above options:

Statement 1 : They are prime
2 and 3 are prime numbers but 3 and 4 are not prime though they are co-prime (Refer Statement (d) above).
Therefore Statement 1 not always True.

Statement 2 : They are consecutive.
2 and 3 are consecutive but 3 and 5 are not consecutive though they are Co-prime ( Refer Statement (B) above).
Therefore Statement 2 is not always true.

Statement 3 : They do not have a common prime factor
This is always True. It is the basic definition of all co-prime numbers.

Statement 4: They do not have a common factor other than 1
This is always True. Again it is the basic definition of all Co-prime Numbers.

Only Statements 3 and 4 are always true.
Non-Human User
Joined: 09 Sep 2013
Posts: 13279
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

### Show Tags

20 Feb 2019, 08:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic   [#permalink] 20 Feb 2019, 08:23
Display posts from previous: Sort by