good GCD -LCM question

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lunar: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Thu May 15, 2014 5:29 am

by lunar » Sun Nov 06, 2016 5:53 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 and II only
(B) III only
(C) I, V only
(D) I,II, III, V only
(E) I, II, III, IV, V

Answer to above question is B

I have understood 4 the answer choices but i have failed to understand V part only . Kindly anybody help me on this . Not able to understand at all

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Sun Nov 06, 2016 11:25 am

A>1 and B>1
GCD = 1

A and B can take multiple values but lets take two conditions
let A=22,B=3 or A=33,B=7 such that GCD = 1

1) A and B are prime numbers-false
2) A and B are consecutive numbers - false
3) A and B dont have common prime numbers - true, that's why GCD = 1
4) Product of two numbers are prime - false
5) A and B are opposite odd-even numbers-false

A and B cannot be both even else their GCD will be 2
but both can be odd/even or odd/odd
odd/even A = 33 and B = 2 GCD = 1
odd/odd A = 3 and B = 77 GCD = 1

only 3rd condition is correct

SO B

Fiza Gupta

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by [email protected] » Sun Nov 06, 2016 11:56 am

Hi lunar,

What is the source of this question? I ask because it has some 'design problems' that don't match up with what you'll see on the Official GMAT. Here's how you can solve it though (while avoiding almost all of the implied work):

We're told that A and B are POSITIVE INTEGERS greater than 1 and that the greatest common divisor is 1. The prompt asks which of the following MUST be true.

Roman Numeral 1: A and B are PRIME numbers.

IF... A=4 and B=7, then the GCD is 1. However, both numbers are not prime, so Roman Numeral 1 is NOT true. We can then eliminate answers A, C, D and E.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Mon Nov 07, 2016 12:40 pm

[email protected] wrote:Hi lunar,

What is the source of this question? I ask because it has some 'design problems' that don't match up with what you'll see on the Official GMAT. Here's how you can solve it though (while avoiding almost all of the implied work):

We're told that A and B are POSITIVE INTEGERS greater than 1 and that the greatest common divisor is 1. The prompt asks which of the following MUST be true.

Roman Numeral 1: A and B are PRIME numbers.

IF... A=4 and B=7, then the GCD is 1. However, both numbers are not prime, so Roman Numeral 1 is NOT true. We can then eliminate answers A, C, D and E.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

In your example, you wrote 'both numbers are not prime'. However, you put B=7 which is prime number

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lunar: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Thu May 15, 2014 5:29 am

by lunar » Mon Nov 07, 2016 6:39 pm

can any expert or forum member explain what is meant by opposite odd-even nature as mentioned in option V

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Nov 07, 2016 10:43 pm

Mo2men wrote:
[email protected] wrote:Hi lunar,

What is the source of this question? I ask because it has some 'design problems' that don't match up with what you'll see on the Official GMAT. Here's how you can solve it though (while avoiding almost all of the implied work):

We're told that A and B are POSITIVE INTEGERS greater than 1 and that the greatest common divisor is 1. The prompt asks which of the following MUST be true.

Roman Numeral 1: A and B are PRIME numbers.

IF... A=4 and B=7, then the GCD is 1. However, both numbers are not prime, so Roman Numeral 1 is NOT true. We can then eliminate answers A, C, D and E.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Hi Rich,

In your example, you wrote 'both numbers are not prime'. However, you put B=7 which is prime number :)

Hi Mo2men,

I think you misunderstand the point that I was trying to make. Roman Numeral 1 states "A AND B are prime numbers", so if you can come up with an example in which they're both NON-primes OR just one is a prime, then you've disproven that Roman Numeral. In my example, I used one prime and one non-prime, so... BOTH numbers are not prime.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Nov 11, 2016 3:27 pm

lunar wrote:can any expert or forum member explain what is meant by opposite odd-even nature as mentioned in option V

It seems to be a poorly-worded way of saying that A is even, B is odd, or vice versa. (A better way of saying this might be "A and B have different parities" or "A and B have distinct remainders when divided by 2".)

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Nov 11, 2016 3:29 pm

A quick way of solving this:

In this case (since the GCF is 1), I implies III, so if I is true, III must be true. That eliminates A and C.

From here, test III exclusive of I. If A = 3 and B = 4, we satisfy the conditions, so I need not be true.

That leaves us with B, so we're set!

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