NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 22:10 It is currently 23 Apr 2024, 22:10
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16831 [13]
Given Kudos: 165
Send PM
What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink] New post   07 Jun 2018, 22:44
13
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

55% (02:16) correct 45% (02:15) wrong based on 239 sessions
Hide Show 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.
ShowHide Answer
Official Answer
E
User avatar
B
jackspire
Manager
Manager
Joined: 22 Sep 2017
Posts: 135
Own Kudos [?]: 34 [0]
Given Kudos: 97
Send PM
Re: What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink] 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.
avatar
B
nithinjohn
Intern
Intern
Joined: 20 Feb 2017
Status:Rise above
Posts: 42
Own Kudos [?]: 84 [1]
Given Kudos: 37
Location: India
Schools: ESSEC '22
GMAT 1: 650 Q47 V34
GPA: 3
WE:Editorial and Writing (Entertainment and Sports)
Send PM
What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink] New post   08 Jun 2018, 22:17
1
Kudos
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.
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16831 [2]
Given Kudos: 165
Send PM
Re: What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink] New post   11 Jun 2018, 06:22
1
Kudos
1
Bookmarks
Expert Reply

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
User avatar
G
aserghe1
Manager
Manager
Joined: 30 Mar 2017
Posts: 88
Own Kudos [?]: 147 [0]
Given Kudos: 53
GMAT 1: 200 Q1 V1
Send PM
Reviews Badge
Re: What is the GCD of the numbers 3, a, and 12, if ‘a’ is an integer [#permalink] New post   23 Jun 2018, 12:40
What is the GCD of 3,a,12, where a ≥ 3? This is the same as what is the GCD of 3 and a?
If a is a multiple of 3, answer will be 3. If a is not a multiple of 3, answer will be 1.

(1)
a is a prime greater than 2.
If a=3, GCD=3
If a=5, GCD=1
Not suff

(2)
a=3 and a=5 also fit here.

Answer: E
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32634
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: What is the GCD of the numbers 3, a, and 12, if a is an integer [#permalink] New post   02 Aug 2023, 22:40
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.
GMAT Club Bot
gmatclubot
Re: What is the GCD of the numbers 3, a, and 12, if a is an integer [#permalink]
02 Aug 2023, 22:40
Moderator:
Bunuel
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions