If A and B are positive integers greater than 1 such that

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Mon Mar 19, 2018 7:23 am

If A and B are positive integers greater than 1 such that the GCD of A and B is 1, then which of the following must be true?

I. A and B are prime numbers.

II. A and B are consecutive numbers.

III. A and B do not have a common prime factor

IV. The product AB has two prime factors

V. A and B have the opposite even-odd nature

A. I & II only
B. III only
C. I, V only
D. I, II, III, V only
E. I, II, III, IV & V

OA is B

I got this question through process of elimination. Once i was able to figure out that I. is not the answer, i was able to eliminate A,C,D, and E which has I. So, i selected B.
However, while i was reviewing, i was not able to understand V.
V. says A and B have opposite even-odd nature. To this statement i undertood that A = 2 and B = 9, which is TRUE
But, It could also be A = 3 and B = 5, which is FALSE.

Kindly, please let me know about V.

Thanks

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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 » Mon Mar 19, 2018 9:39 am

vinni.k wrote:If A and B are positive integers greater than 1 such that the GCD of A and B is 1, then which of the following must be true?

I. A and B are prime numbers.

II. A and B are consecutive numbers.

III. A and B do not have a common prime factor

IV. The product AB has two prime factors

V. A and B have the opposite even-odd nature

A. I & II only
B. III only
C. I, V only
D. I, II, III, V only
E. I, II, III, IV & V

If A=3*5=15 and B=7*11=77, then I, II, IV, and V are not true.
Since I, II, IV and V do not have to be true, eliminate any answer choice that includes I, II, IV and V.
Eliminate A, C, D and E.

The correct answer is B.

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by [email protected] » Mon Mar 19, 2018 2:50 pm

Hi vinni.k,

We're told that A and B are positive integers greater than and that the Greatest Common Divisor of A and B is 1. We're asked which of the following MUST be true (which really means "which of the following is ALWAYS TRUE no matter how many different examples we come up with?"). This question can be solved by TESTing VALUES and doing just a little bit of work.

To start, there are LOTS of different pairs of values that you can choose for A and B, but you might have to consider more than just the first option that comes to mind.

I. A and B are prime numbers.

Your first example might be A=2, B=3. With A=4, B=5 though, Roman Numeral 1 is NOT always true. At this point, you can eliminate ALL 4 wrong answers.

Final Answer: B

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Tue Mar 20, 2018 8:29 am

Rich and Mitch,

Thanks for your reply.
I also did exactly the same way and got the answer. My real problem is :- how do you interpret "A and B have the opposite even-odd nature " (last answer option).

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Wed Mar 21, 2018 8:37 am

Hello Experts,

Please reply on this doubt. I will really appreciate it.
Do you think the interpretation of this statement "A and B have the opposite even-odd nature" is correct ?

To this statement i undertood that A = 2 and B = 9, which is TRUE
But, It could also be A = 3 and B = 5, which is FALSE.

I have got one more question with the same statement. Please check the bold one below. I just want to know whether i am interpreting it correctly or not.

If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?

(A) A is a prime number
(B) A and B have the same prime factors.
(C)A and B have the same even-odd nature
(D) All the factors of B are divisible by A
(E) The LCM of A and B is B

 Please Please let me know whether i am correct or correct me if i am wrong. Will really appreciate it.

Thanks

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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 » Wed Mar 21, 2018 8:46 am

vinni.k wrote:Hello Experts,

Please reply on this doubt. I will really appreciate it.
Do you think the interpretation of this statement "A and B have the opposite even-odd nature" is correct ?

To this statement i undertood that A = 2 and B = 9, which is TRUE
But, It could also be A = 3 and B = 5, which is FALSE.

I have got one more question with the same statement. Please check the bold one below. I just want to know whether i am interpreting it correctly or not.

If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?

(A) A is a prime number
(B) A and B have the same prime factors.
(C)A and B have the same even-odd nature
(D) All the factors of B are divisible by A
(E) The LCM of A and B is B

 Please Please let me know whether i am correct or correct me if i am wrong. Will really appreciate it.

Thanks

Yes you are correct.
The statement tells us that EITHER both integers are odd OR both integers are even.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Wed Mar 21, 2018 10:25 am

Thanks Brent

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