If q is a member of the set {21, 22, 24, 25, 26, 27}

[VJesus12]

If q is a member of the set {21, 22, 24, 25, 26, 27} what is the value of q?

(1) q has exactly 1 prime factor
(2) q is divisible by 3

The OA is C.

I don't know how to prove that the correct answer is the option C. I believe is E. May someone clarifies this for me?

[GMATGuruNY]

If q is a member of the set {21, 22, 24, 25, 26, 27} what is the value of q?

(1) q has exactly 1 prime factor
(2) q is divisible by 3

Statement 1:
Here, there are exactly two options for q:
Case 1: q=25, since the only prime factor of 25 is 5.
Case 2: q=27, since the only prime factor of 27 is 3.
Since q can be different values, INSUFFICIENT.

Statement 2:
Here, there are exactly two options for q:
Case 2: q=27, since 27 is divisible by 3.
Case 3 and 4: q=21 or q=24, since both values are divisible by 3.
Since q can be different values, INSUFFICIENT.

Statements combined:
Both statements are satisfied only by Case 2.
In Case 2, q=27.
SUFFICIENT.

The correct answer is C.

[Vincen]

Hi Vjesus12.

I would solve this question as follows:

Let's call A={21, 22, 24, 25, 26, 27}. The prime factorization of the elements of A are:

21 = 3*7
22 = 2*11
24 = 2*2*2*3
25 = 5*5
26 = 2*13
27 = 3*3*3

(1) q has exactly 1 prime factor

Watching the list, we can see that there are two options for q : 25 and 27. Hence, this statement is NOT SUFFICIENT.

(2) q is divisible by 3

Again, there are 3 different options for q : 21, 24 and 27. Hence, this statement is NOT SUFFICIENT.

Using both statements together

The unique number that is in the statement (1) and also is in the statement (2) is q=27. Hence, both statements together are SUFFICIENT.

I hope this answer may help you.

[Jeff@TargetTestPrep]

If q is a member of the set {21, 22, 24, 25, 26, 27} what is the value of q?

(1) q has exactly 1 prime factor
(2) q is divisible by 3

We need to determine the value of q given that q is a member of the set {21, 22, 24, 25, 26, 27}.

Statement One Alone:

q has exactly 1 prime factor.

If that is the case, the q is either a prime or a power of a prime. We see that none of the integers in the set is prime, however, both 25 and 27 are a power of a prime (25 = 5^2 and 27 = 3^3). Since q can be either 25 or 27, statement one alone is not sufficient.

Statement Two Alone:

q is divisible by 3.

We see that 21, 24, and 27 are divisible by 3, so q can be any one of these integers. Statement two alone is not sufficient.

Statements One and Two Together:

Using statements one and two, we see that q must be 27.

Answer: C