If k is a prime number, what is the value of k?

Question

(1) 3k is a common factor of 24 and 36.
(2) k is a factor of 6.

DavidTutorexamPAL · Answer

As the numbers we're given are relatively small, instead of looking for an abstract solution we'll just list all our options.
This is an Alternative solution.

(1) If 3k is a factor of 24 then k is a factor of 8. Then it could be 1,2,4 or 8 but since it is prime it must equal 2.
If 3k is a factor of 36 then k is a factor of 12. So k = 1,2,3,4,6,12 but since it is prime it must equal 2 or 3.
Then k = 2.
Sufficient!

(2) The factors of 6 are 1,2,3,6. k is prime so it can be 2 or 3.
Insufficient!

(A) is our answer.

Tulkin987 · Answer

(1) Common factors of  24  and  36  are  1, 2, 3, 4, 6, 12 . So,  k  can be  \frac{1}{3}, \frac{2}{3}, 1, \frac{4}{3}, 2, 4 . Among these, only  2  is a prime number and  k=2 , hence suff.

(2)  k  can be  2  or  3 . Not suff

Answer: A

KSBGC · Answer

It's given that K is a prime number. we have to find out what is the value of K.

statement 1: it states that 3k is a factor of 24 and 36. Now just think if k is a prime k could be 2 3 5 7 11 13 and so on. here it is better to input some primes. if k=2 , 3k will be 6 which is a factor of both 24 and 36. If k = 3 we will get 9 but it is not a factor of 24. we need to pick up a value for k that ultimately divides both 24 and 26. It is only possible if we take 2 as a value of K. Sufficient. thus the value of k is 2.

statement 2: it states that k is a factor of 6. Factors of 6 are : 1, 2, 3 , 6. now it is given that k is a prime. we are left with 2 and 3. Thus, we can pick up the specific one. Not stuff.

Thus the correct answer is A.

If k is a prime number, what is the value of k?

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