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

It is currently 18 Jun 2018, 21:43

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1498
What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink]

Show Tags

New post 07 Jun 2018, 22:44
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

29% (01:11) correct 71% (01:47) wrong based on 35 sessions

HideShow timer Statistics

What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer and a ≥ 3?

    1. ‘a’ is a prime number greater than 2.
    2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.

_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
avatar
B
Joined: 22 Sep 2017
Posts: 53
Re: What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink]

Show Tags

New post 08 Jun 2018, 08:25
EgmatQuantExpert wrote:
What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer and a ≥ 3?

    1. ‘a’ is a prime number greater than 2.
    2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.



Option-1 - "a" can have any number greater than or equal to 3. So we can't determine the exact GCD(3,a,12). Insufficient.
Option-2 - Here "a" can have values such as 5, 6 and 10. In all cases GCD(3,a) and LCM(3,a) are factors of 30. So we can't derive exact value of GCD(3,a,12). Insufficient.

Now, combining both options we will have only one value of "a=5" as 5 is the only prime number greater than 2. So we can find out the exact value of GCD now.
So, the answer is C.
Intern
Intern
avatar
B
Status: Rise above
Joined: 20 Feb 2017
Posts: 23
Location: India
GMAT 1: 650 Q47 V34
WE: Editorial and Writing (Entertainment and Sports)
What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink]

Show Tags

New post 08 Jun 2018, 22:17
jackspire wrote:
EgmatQuantExpert wrote:
What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer and a ≥ 3?

    1. ‘a’ is a prime number greater than 2.
    2. Both GCD (3, a) and LCM (3, a) are factors of the number 30.



Option-1 - "a" can have any number greater than or equal to 3. So we can't determine the exact GCD(3,a,12). Insufficient.
Option-2 - Here "a" can have values such as 5, 6 and 10. In all cases GCD(3,a) and LCM(3,a) are factors of 30. So we can't derive exact value of GCD(3,a,12). Insufficient.

Now, combining both options we will have only one value of "a=5" as 5 is the only prime number greater than 2. So we can find out the exact value of GCD now.
So, the answer is C.

What if we consider a=3? then GCD of (3,3) =3 and LCm of (3,3) =3 which is a factor of 30. Hence answer should be E in my opinion.
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1498
Re: What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink]

Show Tags

New post 11 Jun 2018, 06:22

Solution



Given:
    • a is an integer
    • a ≥ 3

To find:
    • The GCD of (3, a, 12)

Analysing Statement 1
    • As per the information given in statement 1, ‘a’ is a prime number greater than 2
      o Therefore, ‘a’ can have values like 3, 5, 7, 11 etc

    • If a = 3, GCD (3, a, 12) = GCD (3, 3, 12) = 3
    • If a = 5, GCD (3, a, 12) = GCD (3, 5, 12) = 1
    • If a = 7, GCD (3, a, 12) = GCD (3, 7, 12) = 1

We can see, for different values of a, we are getting different GCD values

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, both GCD (3, a) and LCM (3, a) are factors of the number 30
      o Factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30

    • If a = 3, GCD (3, a) = GCD (3, 3) = 1 and LCM (3, 3) = 3
      o Both 1 and 3 are factors of 30
      o Also, GCD (3, a, 12) = GCD (3, 3, 12) = 3

    • If a = 5, GCD (3, a) = GCD (3, 5) = 1 and LCM (3, 5) = 15
      o Both 1 and 15 are factors of 30
      o Also, (3, a, 12) = GCD (3, 5, 12) = 1

We can see a can have multiple possible values which satisfy the given statement, and the GCD of (3, a, 12) is different for different values of a

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Even after combining the statements, we can say
    • a can be 3 or 5, for which GCD is different – hence unique value of a cannot be determined

Hence, the correct answer is option E.

Answer: E
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer   [#permalink] 11 Jun 2018, 06:22
Display posts from previous: Sort by

What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.