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

Question

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.

jackspire · Answer

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.

nithinjohn · Answer

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.

EgmatQuantExpert · Answer

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

aserghe1 · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards