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

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

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New post 19 Nov 2014, 01:47
1
1
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A
B
C
D
E

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Question Stats:

60% (01:32) correct 40% (01:27) wrong based on 70 sessions

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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
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

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New post 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?
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

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New post 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.
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

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New post 19 Nov 2014, 02:41
ok fine; seems I got confused in between solving it.......
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

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New post 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.

Experts please confirm.
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

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New post 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.
Therefore Answer is C
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic  [#permalink]

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New post 20 Feb 2019, 08:23
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Re: If GCD of two numbers (both integers, greater than 1) is 1, then whic   [#permalink] 20 Feb 2019, 08:23
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